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Search: a209913 -id:a209913
Displaying 1-8 of 8 results found. page 1
     Sort: relevance | references | number | modified | created      Format: long | short | data
A209906 Half the number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having two or four distinct clockwise edge differences. +10
1
62, 562, 5008, 44770, 399930, 3573388, 31926146, 285247762, 2548561164, 22770302450, 203442764450, 1817673135676, 16240122477074, 145098465897778, 1296391988417932, 11582701309989362, 103486422895200258 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 1 of A209913.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 7*a(n-1) + 21*a(n-2) - 30*a(n-3) - 30*a(n-4) + 12*a(n-5) + 8*a(n-6).
Empirical g.f.: 2*x*(31 + 64*x - 114*x^2 - 114*x^3 + 46*x^4 + 32*x^5) / (1 - 7*x - 21*x^2 + 30*x^3 + 30*x^4 - 12*x^5 - 8*x^6). - Colin Barker, Jul 13 2018
EXAMPLE
Some solutions for n=4:
..0..2....1..2....0..2....2..0....0..0....0..0....3..0....2..0....2..3....1..0
..0..3....0..3....3..3....2..3....1..3....2..3....1..0....3..0....0..1....0..1
..0..1....2..2....0..1....1..2....2..1....3..2....0..3....2..0....2..0....0..3
..2..3....0..3....2..3....0..1....3..2....0..1....2..3....3..1....0..1....1..2
..1..2....2..2....2..0....1..2....0..3....0..3....1..2....1..2....3..0....2..1
CROSSREFS
Cf. A209913.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 15 2012
STATUS
approved
A209907 Half the number of (n+1)X3 0..3 arrays with every 2X2 subblock having two or four distinct clockwise edge differences +10
1
562, 13098, 295448, 6711168, 152153160, 3452051294, 78298719958, 1776153151954, 40289004709802, 913904480044196, 20730591242525088, 470244787257936734, 10666837893533545782, 241962270764619764754, 5488573721848784927246 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 2 of A209913
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 16*a(n-1) +227*a(n-2) -1440*a(n-3) -8244*a(n-4) +46409*a(n-5) +53926*a(n-6) -406100*a(n-7) -117231*a(n-8) +1484559*a(n-9) +166049*a(n-10) -2587430*a(n-11) -386782*a(n-12) +2096907*a(n-13) +472125*a(n-14) -660956*a(n-15) -166954*a(n-16) +44616*a(n-17) +4488*a(n-18) -192*a(n-19)
EXAMPLE
Some solutions for n=4
..3..0..1....3..0..0....2..2..1....1..2..3....3..0..1....3..3..1....1..1..3
..2..0..3....1..1..3....3..0..2....2..3..1....1..3..0....1..0..3....0..3..0
..1..2..0....3..0..3....0..3..3....1..2..3....2..1..1....2..3..0....0..1..0
..2..0..3....2..0..1....1..0..2....3..1..2....1..3..0....1..2..1....0..3..1
..0..2..0....2..3..1....1..3..2....3..0..3....3..0..1....2..1..2....3..0..0
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 15 2012
STATUS
approved
A209908 Half the number of (n+1)X4 0..3 arrays with every 2X2 subblock having two or four distinct clockwise edge differences +10
1
5008, 295448, 16664508, 948609890, 53888573444, 3063300023090, 174099838817590, 9895452271443782, 562424112112339274, 31966511730858090194, 1816877220289293917242, 103265735487005016409152 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 3 of A209913
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 55*a(n-1) +923*a(n-2) -47071*a(n-3) -231407*a(n-4) +15527254*a(n-5) +7880250*a(n-6) -2573669497*a(n-7) +3681229288*a(n-8) +249190408738*a(n-9) -579450712511*a(n-10) -15545777999632*a(n-11) +42210038348626*a(n-12) +666118006004289*a(n-13) -1886332941998678*a(n-14) -20450809195283436*a(n-15) +57107262824986158*a(n-16) +462837772656461540*a(n-17) -1233589210852233412*a(n-18) -7872410572016992734*a(n-19) +19630990804163291243*a(n-20) +101986218315556639540*a(n-21) -235100512508203944296*a(n-22) -1015682793390488125566*a(n-23) +2150002789746681905996*a(n-24) +7825721744951506498234*a(n-25) -15163164422139297144181*a(n-26) -46841616343312521746791*a(n-27) +82995111044360045734710*a(n-28) +218301161066990302616716*a(n-29) -353790955288161781138915*a(n-30) -792601249983629087376567*a(n-31) +1175946145985688378644800*a(n-32) +2239982343619860900022721*a(n-33) -3045446389006222439252829*a(n-34) -4916701577362858573256478*a(n-35) +6130589140664657413790376*a(n-36) +8353918309455200803527969*a(n-37) -9556132008935803121684739*a(n-38) -10939049915929290500808672*a(n-39) +11474688682455975032157676*a(n-40) +10978124927194304878629570*a(n-41) -10543831886760113161536049*a(n-42) -8383988700731830638859763*a(n-43) +7352253368826483234978608*a(n-44) +4826725129284052501397921*a(n-45) -3849463056922623709810553*a(n-46) -2067854150675962492097465*a(n-47) +1492952670444499632838573*a(n-48) +647468497254091793151276*a(n-49) -421469451029786639157580*a(n-50) -144455861921375175788532*a(n-51) +84661307211707006760020*a(n-52) +22156825180654649239287*a(n-53) -11740439782116785076012*a(n-54) -2219666541575216243128*a(n-55) +1077870975515912576792*a(n-56) +134607253301714192944*a(n-57) -61608386055612989120*a(n-58) -4358301391935808576*a(n-59) +1995845043302066048*a(n-60) +56288530795526656*a(n-61) -31330477096792576*a(n-62) +102010241398784*a(n-63) +162473872068608*a(n-64) -2652426567680*a(n-65)
EXAMPLE
Some solutions for n=4
..1..2..0..2....3..0..0..2....3..0..3..3....0..0..1..0....1..0..0..0
..0..1..2..3....1..3..2..0....0..1..0..1....1..3..3..3....0..3..1..3
..2..3..1..2....1..0..2..3....2..3..0..3....0..0..1..0....1..0..1..0
..1..2..3..1....1..3..2..0....0..1..1..0....2..3..1..3....1..3..3..1
..0..3..0..0....0..0..1..2....3..3..0..3....0..3..0..3....1..0..1..2
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 15 2012
STATUS
approved
A209909 Half the number of (n+1)X5 0..3 arrays with every 2X2 subblock having two or four distinct clockwise edge differences +10
1
44770, 6711168, 948609890, 135833193008, 19391662870652, 2771380588485262, 395928291655518846, 56572313966664992566, 8082834582799800606818, 1154877996377518700415076, 165007101830680869540237766 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 4 of A209913
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=4
..1..1..3..3..0....3..0..0..1..1....0..2..2..1..0....1..0..0..0..0
..3..0..1..0..2....1..3..1..3..0....3..3..0..2..3....3..1..3..1..3
..1..1..2..1..3....0..0..3..1..1....0..1..3..3..2....1..3..1..3..0
..3..0..1..0..2....3..1..0..0..3....3..1..0..1..3....1..0..3..0..1
..1..3..2..1..3....0..3..3..2..2....3..0..1..3..1....0..1..1..0..3
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 15 2012
STATUS
approved
A209910 Half the number of (n+1)X6 0..3 arrays with every 2X2 subblock having two or four distinct clockwise edge differences +10
1
399930, 152153160, 53888573444, 19391662870652, 6954596004028468, 2497054784947973388, 896278100477366851795, 321743305461455008300382, 115494087693753318505527463, 41458747023669964452852387044 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 5 of A209913
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=4
..3..1..3..1..0..0....2..2..3..1..1..2....1..0..0..1..0..3....1..2..1..3..2..1
..3..0..1..2..1..3....3..0..3..0..3..1....2..1..3..0..1..3....3..1..3..1..0..2
..1..1..3..1..3..2....0..1..1..1..1..2....1..3..0..1..0..1....1..0..3..0..3..3
..0..3..0..0..1..0....2..3..0..3..0..3....3..2..3..1..3..2....3..2..2..3..1..0
..1..2..2..3..3..2....0..0..3..0..3..2....2..1..2..3..2..0....0..0..3..0..3..0
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 15 2012
STATUS
approved
A209911 Half the number of (n+1)X7 0..3 arrays with every 2X2 subblock having two or four distinct clockwise edge differences +10
1
3573388, 3452051294, 3063300023090, 2771380588485262, 2497054784947973388, 2253166071062026531552, 2032217168415654090395276, 1833259667261950945314036728, 1653671485554060485462472516346 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 6 of A209913
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=4
..1..1..1..0..3..2..3....0..1..1..1..1..3..3....2..3..2..1..0..2..1
..3..0..3..2..2..3..2....3..3..0..3..0..2..0....0..3..0..2..3..3..2
..0..1..0..3..0..2..1....0..1..0..1..3..0..2....1..0..2..3..2..0..3
..3..0..1..1..3..3..0....1..3..2..0..3..2..0....1..3..2..0..2..3..2
..2..2..3..0..0..1..1....2..1..3..3..1..0..3....3..1..3..0..3..0..2
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 15 2012
STATUS
approved
A209912 Half the number of (n+1) X 8 0..3 arrays with every 2 X 2 subblock having two or four distinct clockwise edge differences. +10
1
31926146, 78298719958, 174099838817590, 395928291655518846, 896278100477366851795, 2032217168415654090395276, 4605826850905941430535864352, 10440431207754050038448850990818 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 7 of A209913.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=4
..3..3..2..0..0..2..1..1....0..2..3..2..3..3..2..3....3..2..0..3..3..3..2..3
..0..1..0..1..3..3..0..3....0..3..1..3..0..2..3..0....0..0..3..0..1..0..1..0
..0..3..3..0..1..0..1..3....2..2..0..1..3..2..0..2....2..3..0..1..0..1..0..3
..2..0..1..3..0..1..0..0....3..0..1..0..2..1..2..3....3..0..3..1..3..1..3..0
..0..1..3..0..1..2..3..1....3..1..3..3..3..0..1..0....3..1..1..2..1..0..1..1
CROSSREFS
Cf. A209913.
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 15 2012
STATUS
approved
A209905 Half the number of (n+1)X(n+1) 0..3 arrays with every 2X2 subblock having two or four distinct clockwise edge differences +10
0
62, 13098, 16664508, 135833193008, 6954596004028468, 2253166071062026531552, 4605826850905941430535864352, 59470527831535893681344131012059952 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Diagonal of A209913
LINKS
Table of n, a(n) for n=1..8.
EXAMPLE
Some solutions for n=4
..0..2..2..1..0....3..0..3..3..0....1..0..0..0..0....3..0..0..1..1
..3..3..0..2..3....0..3..0..1..3....3..1..3..1..3....1..3..1..3..0
..0..1..3..3..2....1..0..1..0..1....1..3..1..3..0....0..0..3..1..1
..3..1..0..1..3....1..3..3..2..3....1..0..3..0..1....3..1..0..0..3
..3..0..1..3..1....2..1..0..0..3....0..1..1..0..3....0..3..3..2..2
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 15 2012
STATUS
approved
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Last modified August 30 13:06 EDT 2024. Contains 375543 sequences. (Running on oeis4.)