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A253007 Number of n X 4 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value increasing by 0 or 1 with every step right, diagonally se or down. 1
1, 1, 1, 1, 124, 3423, 33533, 158877, 490403, 1156178, 2286874, 4013538, 6467242, 9779058, 14080058, 19501314, 26173898, 34228882, 43797338, 55010338, 67998954, 82894258, 99827322, 118929218, 140331018, 164163794, 190558618, 219646562 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

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

FORMULA

Empirical: a(n) = (65536/3)*n^3 - 422912*n^2 + (8343128/3)*n - 6208382 for n>9.

Conjectures from Colin Barker, Dec 08 2018: (Start)

G.f.: x*(1 - 3*x + 3*x^2 - x^3 + 123*x^4 + 2930*x^5 + 20582*x^6 + 44788*x^7 + 42525*x^8 + 17119*x^9 + 2605*x^10 + 375*x^11 + 25*x^12) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>13.

(End)

EXAMPLE

Some solutions for n=6:

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

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

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

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

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

..2..2..2..2....1..1..2..2....1..2..2..2....1..1..1..2....1..1..2..2

CROSSREFS

Column 4 of A253011.

Sequence in context: A260097 A232796 A263544 * A293084 A289299 A035816

Adjacent sequences:  A253004 A253005 A253006 * A253008 A253009 A253010

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 25 2014

STATUS

approved

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Last modified June 19 12:57 EDT 2019. Contains 324222 sequences. (Running on oeis4.)