The On-Line Encyclopedia of Integer Sequences (OEIS)

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A252820

T(n,k)=Number of nXk nonnegative integer arrays with upper left 0 and every value within 2 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down
(history; published version)

#4 by R. H. Hardin at Mon Dec 22 10:52:57 EST 2014

STATUS

editing

approved

#3 by R. H. Hardin at Mon Dec 22 10:52:53 EST 2014

LINKS

R. H. Hardin, <a href="/A252820/b252820.txt">Table of n, a(n) for n = 1..1680</a>

#2 by R. H. Hardin at Mon Dec 22 10:51:56 EST 2014

NAME

allocated for R. H. Hardin

T(n,k)=Number of nXk nonnegative integer arrays with upper left 0 and every value within 2 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down

DATA

1, 2, 2, 4, 6, 4, 7, 17, 17, 7, 11, 40, 63, 40, 11, 16, 81, 187, 187, 81, 16, 22, 147, 468, 684, 468, 147, 22, 29, 246, 1032, 2078, 2078, 1032, 246, 29, 37, 387, 2067, 5490, 7564, 5490, 2067, 387, 37, 46, 580, 3840, 13015, 23664, 23664, 13015, 3840, 580, 46, 56, 836, 6716

OFFSET

1,2

COMMENTS

Table starts

..1...2.....4......7.....11......16.......22........29........37.........46

..2...6....17.....40.....81.....147......246.......387.......580........836

..4..17....63....187....468....1032.....2067......3840......6716......11179

..7..40...187....684...2078....5490....13015.....28299.....57338.....109549

.11..81...468...2078...7564...23664....65711....165685....385736.....839799

.16.147..1032...5490..23664...86724...279300....809349...2147638....5289321

.22.246..2067..13015..65711..279300..1033761...3414257..10248688...28359679

.29.387..3840..28299.165685..809349..3414257..12755742..43017980..132916561

.37.580..6716..57338.385736.2147638.10248688..43017980.161986236..555724696

.46.836.11179.109549.839799.5289321.28359679.132916561.555724696.2106102800

FORMULA

Empirical for column k:

k=1: a(n) = (1/2)*n^2 - (1/2)*n + 1

k=2: a(n) = (1/24)*n^4 + (5/12)*n^3 - (1/24)*n^2 + (7/12)*n + 1

k=3: [polynomial of degree 6]

k=4: [polynomial of degree 8]

k=5: [polynomial of degree 10]

k=6: [polynomial of degree 12]

k=7: [polynomial of degree 14]

Empirical for "within 1" instead of "within 2" is T(n,k)=binomial(n+k,k)-1

EXAMPLE

Some solutions for n=4 k=4

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

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

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

..2..3..4..5....1..2..3..4....1..2..3..4....2..3..4..4....2..2..3..4

CROSSREFS

Column 1 is A000124(n-1)

KEYWORD

allocated

nonn,tabl

AUTHOR

R. H. Hardin, Dec 22 2014

STATUS

approved

editing

#1 by R. H. Hardin at Mon Dec 22 10:11:34 EST 2014

NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved