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A252828 T(n,k)=Number of nXk nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down 8
1, 2, 2, 4, 6, 4, 8, 18, 18, 8, 15, 53, 81, 53, 15, 26, 142, 340, 340, 142, 26, 42, 339, 1238, 1920, 1238, 339, 42, 64, 729, 3891, 9075, 9075, 3891, 729, 64, 93, 1437, 10761, 36292, 54376, 36292, 10761, 1437, 93, 130, 2638, 26764, 125892, 271846, 271846, 125892 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1....2......4.......8.......15........26.........42..........64...........93

...2....6.....18......53......142.......339........729........1437.........2638

...4...18.....81.....340.....1238......3891......10761.......26764........60988

...8...53....340....1920.....9075.....36292.....125892......387849......1082111

..15..142...1238....9075....54376....271846....1165921.....4396009.....14863460

..26..339...3891...36292...271846...1679072....8807722....40232545....163307844

..42..729..10761..125892..1165921...8807722...55960651...306796310...1481748658

..64.1437..26764..387849..4396009..40232545..306796310..2001017650..11403395172

..93.2638..60988.1082111.14863460.163307844.1481748658.11403395172..76084625352

.130.4568.129236.2777103.45791493.598768118.6411737114.57777817522.448101581256

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..721

FORMULA

Empirical for column k:

k=1: a(n) = (1/6)*n^3 - (1/2)*n^2 + (4/3)*n

k=2: [polynomial of degree 6]

k=3: [polynomial of degree 9]

k=4: [polynomial of degree 12]

k=5: [polynomial of degree 15]

k=6: [polynomial of degree 18]

k=7: [polynomial of degree 21]

Empirical for "within 1" instead of "within 3" is T(n,k)=binomial(n+k,k)-1

EXAMPLE

Some solutions for n=4 k=4

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

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

..0..1..2..3....2..3..3..4....1..2..2..3....0..1..2..2....1..1..2..2

..1..2..3..4....3..3..3..4....2..2..2..3....1..2..2..3....1..2..2..3

CROSSREFS

Column 1 is A000125(n-1)

Sequence in context: A096466 A088965 A059474 * A208314 A078099 A264872

Adjacent sequences:  A252825 A252826 A252827 * A252829 A252830 A252831

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 22 2014

STATUS

approved

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Last modified October 23 04:06 EDT 2021. Contains 348211 sequences. (Running on oeis4.)