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A307393 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. ((1-x)^(k-4))/((1-x)^k-x^k). 4
1, 1, 5, 1, 4, 16, 1, 4, 11, 42, 1, 4, 10, 26, 99, 1, 4, 10, 21, 57, 219, 1, 4, 10, 20, 42, 120, 466, 1, 4, 10, 20, 36, 84, 247, 968, 1, 4, 10, 20, 35, 64, 169, 502, 1981, 1, 4, 10, 20, 35, 57, 120, 340, 1013, 4017, 1, 4, 10, 20, 35, 56, 93, 240, 682, 2036, 8100 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
A(n,k) = Sum_{j=0..floor(n/k)} binomial(n+3,k*j+3).
A(n,2*k) = Sum_{i=0..n} Sum_{j=0..n-i} binomial(i+1,k*j+1) * binomial(n-i+1,k*j+1).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
5, 4, 4, 4, 4, 4, 4, 4, ...
16, 11, 10, 10, 10, 10, 10, 10, ...
42, 26, 21, 20, 20, 20, 20, 20, ...
99, 57, 42, 36, 35, 35, 35, 35, ...
219, 120, 84, 64, 57, 56, 56, 56, ...
466, 247, 169, 120, 93, 85, 84, 84, ...
968, 502, 340, 240, 165, 130, 121, 120, ...
MATHEMATICA
T[n_, k_] := Sum[Binomial[n+3, k*j + 3], {j, 0, Floor[n/k]}]; Table[T[n - k, k], {n, 0, 11}, {k, n, 1, -1}] // Flatten (* Amiram Eldar, May 20 2021 *)
CROSSREFS
Columns 1-5 give A002662(n+3), A125128(n+1), A111927(n+3), A000749(n+3), A139748(n+3).
Sequence in context: A180132 A286593 A242376 * A231923 A105664 A094882
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Apr 07 2019
STATUS
approved

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Last modified May 22 15:18 EDT 2024. Contains 372758 sequences. (Running on oeis4.)