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A306915 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. 1/((1-x)^k-x^k). 8
1, 1, 2, 1, 2, 4, 1, 3, 4, 8, 1, 4, 6, 8, 16, 1, 5, 10, 11, 16, 32, 1, 6, 15, 20, 21, 32, 64, 1, 7, 21, 35, 36, 42, 64, 128, 1, 8, 28, 56, 70, 64, 85, 128, 256, 1, 9, 36, 84, 126, 127, 120, 171, 256, 512, 1, 10, 45, 120, 210, 252, 220, 240, 342, 512, 1024 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Antidiagonals n = 0..139, flattened

FORMULA

A(n,k) = Sum_{j=0..floor(n/k)} binomial(n+k-1,k*j+k-1).

A(n,2*k) = Sum_{i=0..n} Sum_{j=0..n-i} binomial(i+k-1,k*j+k-1) * binomial(n-i+k-1,k*j+k-1). - Seiichi Manyama, Apr 07 2019

EXAMPLE

Square array begins:

     1,   1,   1,   1,   1,    1,    1,    1, ...

     2,   2,   3,   4,   5,    6,    7,    8, ...

     4,   4,   6,  10,  15,   21,   28,   36, ...

     8,   8,  11,  20,  35,   56,   84,  120, ...

    16,  16,  21,  36,  70,  126,  210,  330, ...

    32,  32,  42,  64, 127,  252,  462,  792, ...

    64,  64,  85, 120, 220,  463,  924, 1716, ...

   128, 128, 171, 240, 385,  804, 1717, 3432, ...

   256, 256, 342, 496, 715, 1365, 3017, 6436, ...

CROSSREFS

Columns (1+2),3-9 give A000079, A024495(n+2), A000749(n+3), A049016, A192080, A049017, A290995(n+7), A306939.

Cf. A039912, A101508, A306846, A306913, A306914, A307047, A307078, A307393.

Sequence in context: A306913 A087704 A165092 * A270743 A209750 A156042

Adjacent sequences:  A306912 A306913 A306914 * A306916 A306917 A306918

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Mar 16 2019

STATUS

approved

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Last modified October 15 12:28 EDT 2019. Contains 328026 sequences. (Running on oeis4.)