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A306846
Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. ((1-x)^(k-1))/((1-x)^k-x^k).
11
1, 1, 2, 1, 1, 4, 1, 1, 2, 8, 1, 1, 1, 4, 16, 1, 1, 1, 2, 8, 32, 1, 1, 1, 1, 5, 16, 64, 1, 1, 1, 1, 2, 11, 32, 128, 1, 1, 1, 1, 1, 6, 22, 64, 256, 1, 1, 1, 1, 1, 2, 16, 43, 128, 512, 1, 1, 1, 1, 1, 1, 7, 36, 85, 256, 1024, 1, 1, 1, 1, 1, 1, 2, 22, 72, 170, 512, 2048
OFFSET
0,3
LINKS
FORMULA
A(n,k) = Sum_{j=0..floor(n/k)} binomial(n,k*j).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
2, 1, 1, 1, 1, 1, 1, 1, 1, ...
4, 2, 1, 1, 1, 1, 1, 1, 1, ...
8, 4, 2, 1, 1, 1, 1, 1, 1, ...
16, 8, 5, 2, 1, 1, 1, 1, 1, ...
32, 16, 11, 6, 2, 1, 1, 1, 1, ...
64, 32, 22, 16, 7, 2, 1, 1, 1, ...
128, 64, 43, 36, 22, 8, 2, 1, 1, ...
256, 128, 85, 72, 57, 29, 9, 2, 1, ...
MATHEMATICA
T[n_, k_] := Sum[Binomial[n, k*j], {j, 0, Floor[n/k]}]; Table[T[k, n - k + 1], {n, 0, 11}, {k, 0, n}] // Flatten (* Amiram Eldar, Jun 21 2021 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Mar 13 2019
STATUS
approved