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A252934 Number of n X 4 nonnegative integer arrays with upper left 0 and every value within 3 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
8, 34, 153, 711, 3067, 10920, 30818, 70640, 138558, 242764, 391450, 592808, 855030, 1186308, 1594834, 2088800, 2676398, 3365820, 4165258, 5082904, 6126950, 7305588, 8627010, 10099408, 11730974, 13529900, 15504378, 17662600, 20012758, 22563044 (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) = (4096/3)*n^3 - 18720*n^2 + (269642/3)*n - 149376 for n>6.

Conjectures from Colin Barker, Dec 07 2018: (Start)

G.f.: x*(8 + 2*x + 65*x^2 + 271*x^3 + 1013*x^4 + 2340*x^5 + 2849*x^6 + 1331*x^7 + 293*x^8 + 20*x^9) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>10.

(End)

EXAMPLE

Some solutions for n=4:

..0..0..0..0....0..0..1..1....0..0..1..1....0..0..1..1....0..0..1..1

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

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

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

CROSSREFS

Column 4 of A252938.

Sequence in context: A101644 A126395 A227330 * A229398 A223015 A222796

Adjacent sequences:  A252931 A252932 A252933 * A252935 A252936 A252937

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 24 2014

STATUS

approved

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Last modified April 6 20:39 EDT 2020. Contains 333286 sequences. (Running on oeis4.)