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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

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

Adjacent sequences:  A253218 A253219 A253220 * A253222 A253223 A253224

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 29 2014

STATUS

approved

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Last modified October 16 16:08 EDT 2019. Contains 328101 sequences. (Running on oeis4.)