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A253223 T(n,k)=Number of nXk 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 7
0, 0, 0, 1, 0, 1, 3, 1, 1, 3, 6, 9, 1, 9, 6, 10, 25, 19, 19, 25, 10, 15, 49, 102, 19, 102, 49, 15, 21, 81, 263, 268, 268, 263, 81, 21, 28, 121, 504, 1249, 268, 1249, 504, 121, 28, 36, 169, 825, 3140, 3568, 3568, 3140, 825, 169, 36, 45, 225, 1226, 5986, 16028, 3568, 16028 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Table starts

..0...0....1.....3......6......10......15.......21........28........36

..0...0....1.....9.....25......49......81......121.......169.......225

..1...1....1....19....102.....263.....504......825......1226......1707

..3...9...19....19....268....1249....3140.....5986......9792.....14558

..6..25..102...268....268....3568...16028....40238.....77063....126673

.10..49..263..1249...3568....3568...47698...213155....538444...1039060

.15..81..504..3140..16028...47698...47698...649712...2913793...7415837

.21.121..825..5986..40238..213155..649712...649712...9023385..40680959

.28.169.1226..9792..77063..538444.2913793..9023385...9023385.127419681

.36.225.1707.14558.126673.1039060.7415837.40680959.127419681.127419681

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..2812

FORMULA

Empirical for column k:

k=1: a(n) = (1/2)*n^2 - (3/2)*n + 1

k=2: a(n) = 4*n^2 - 20*n + 25 for n>2

k=3: a(n) = 40*n^2 - 279*n + 497 for n>4

k=4: a(n) = 480*n^2 - 4354*n + 10098 for n>6

k=5: a(n) = 6400*n^2 - 71990*n + 206573 for n>8

k=6: a(n) = 90112*n^2 - 1212288*n + 4150790 for n>10

k=7: a(n) = 1306624*n^2 - 20460244*n + 81385043 for n>12

EXAMPLE

Some solutions for n=4 k=4

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

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

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

..1..1..1..1....1..1..1..1....1..1..1..1....1..1..1..1....1..1..1..1

CROSSREFS

Column 1 is A000217(n-2)

Column 2 is A016754(n-3)

Sequence in context: A133825 A156710 A114588 * A121745 A252983 A089312

Adjacent sequences:  A253220 A253221 A253222 * A253224 A253225 A253226

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 29 2014

STATUS

approved

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Last modified October 4 01:04 EDT 2022. Contains 357237 sequences. (Running on oeis4.)