login
A253221
Number of n X 6 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value within 2 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.
1
10, 49, 263, 1249, 3568, 3568, 47698, 213155, 538444, 1039060, 1719174, 2579462, 3619974, 4840710, 6241670, 7822854, 9584262, 11525894, 13647750, 15949830, 18432134, 21094662, 23937414, 26960390, 30163590, 33547014, 37110662, 40854534
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 90112*n^2 - 1212288*n + 4150790 for n > 10.
Conjectures from Colin Barker, Dec 10 2018: (Start)
G.f.: x*(10 + 19*x + 146*x^2 + 597*x^3 + 561*x^4 - 3652*x^5 + 46449*x^6 + 77197*x^7 + 38505*x^8 + 15495*x^9 + 4171*x^10 + 676*x^11 + 50*x^12) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 13.
(End)
EXAMPLE
Some solutions for n=4:
0 0 1 2 2 3 0 0 0 1 2 3 0 1 1 2 2 3 0 0 1 2 2 3
1 1 1 2 2 3 0 1 1 1 2 3 1 1 1 2 3 3 0 1 1 2 2 3
1 1 1 2 2 3 1 1 2 2 2 3 2 2 2 2 3 3 0 1 2 2 3 3
2 2 2 2 3 3 2 2 2 3 3 3 2 3 3 3 3 3 1 1 2 3 3 3
CROSSREFS
Column 6 of A253223.
Sequence in context: A244864 A051947 A274561 * A222633 A061861 A243226
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 29 2014
STATUS
approved