The On-Line Encyclopedia of Integer Sequences (OEIS)

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A201724

Number of nX3 0..4 arrays with rows and columns lexicographically nondecreasing and no element equal to the number of horizontal and vertical neighbors equal to itself
(history; published version)

#5 by Russ Cox at Sat Mar 31 12:36:45 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Dec 04 2011

Discussion

Sat Mar 31

12:36

OEIS Server: https://oeis.org/edit/global/875

#4 by Ron Hardin at Sun Dec 04 12:23:29 EST 2011

STATUS

editing

approved

#3 by Ron Hardin at Sun Dec 04 12:23:19 EST 2011

LINKS

R. H. Hardin, <a href="/A201724/b201724.txt">Table of n, a(n) for n = 1..210</a>

#2 by Ron Hardin at Sun Dec 04 12:22:55 EST 2011

NAME

allocated for Ron HardinNumber of nX3 0..4 arrays with rows and columns lexicographically nondecreasing and no element equal to the number of horizontal and vertical neighbors equal to itself

DATA

20, 631, 19827, 499474, 9603489, 144262866, 1757594146, 17915547783, 156619023957, 1198133817532, 8153980411514, 50035648469991, 279906963092730, 1440489290975090, 6871449852708897, 30577097006475471, 127620952939695332

OFFSET

1,1

COMMENTS

Column 3 of A201729

FORMULA

Empirical: a(n) = (1143/13339406848768000000)*n^27 + (34659/3334851712192000000)*n^26 - (305829/102610821913600000)*n^25 + (18786617/246265972592640000)*n^24 + (3958894117/102610821913600000)*n^23 - (890060916037/160608242995200000)*n^22 + (3883955751623/13140674426880000)*n^21 + (15789034554253/1946766581760000)*n^20 - (43341713819681471/15162316646400000)*n^19 + (11737791620928206489/41496866611200000)*n^18 - (9354946607145085039/507183925248000)*n^17 + (89620729802927851309/99447828480000)*n^16 - (743803233665752540021073/21816367372800000)*n^15 + (28499385666924665391563347/29088489830400000)*n^14 - (25455135268631407928105381/1342545684480000)*n^13 + (461140646483326049588504801/5370182737920000)*n^12 + (28265806624709228060073236461/2593554163200000)*n^11 - (22551750300604775835503572048823/41496866611200000)*n^10 + (90452907504811296149083077682639/5631717611520000)*n^9 - (3032483358174968127916184659794719/8760449617920000)*n^8 + (393637850170773012106697103526188929/69493951296000000)*n^7 - (7869653987787486349645970604178160087/112927670856000000)*n^6 + (1901252628397296031171310111143845105449/3116803715625600000)*n^5 - (796590434152973474143064866658414914883/249344297250048000)*n^4 + (22209548841602923195409813138654672819/15006832704864000)*n^3 + (75783682547020727035019319582699319129/643149973065600)*n^2 - (1510369517764017479305249768151297/1784742960)*n + 2129912253933134417390679 for n>45

EXAMPLE

Some solutions for n=3

..1..2..4....1..3..4....0..0..1....0..1..3....0..0..4....1..3..4....0..0..1

..2..2..2....3..1..4....1..3..3....0..2..3....0..4..4....2..1..1....1..3..4

..3..0..0....4..2..3....4..1..4....2..3..3....3..2..2....2..1..1....2..4..2

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Dec 04 2011

STATUS

approved

editing

#1 by Ron Hardin at Sun Dec 04 12:16:06 EST 2011

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved