A177993 Triangle read by rows, A177990 * A007318.

1, 1, 1, 2, 3, 1, 2, 4, 3, 1, 3, 8, 9, 5, 1, 3, 9, 13, 11, 5, 1, 4, 15, 28, 31, 20, 7, 1, 4, 16, 34, 46, 40, 22, 7, 1, 5, 24, 62, 102, 110, 78, 35, 9, 1, 5, 25, 70, 130, 166, 148, 91, 37, 9, 1, 6, 35, 115, 250, 376, 400, 301, 157, 54, 11, 1, 6, 36, 125, 295, 496, 610, 553, 367, 174, 56, 11, 1

Offset

0,4

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

Formula

As infinite lower triangular matrices, A177990 * Pascal's triangle, (A007318).

T(n,k) = binomial(n,k) + Sum_{j=0..floor(n/2)-1} binomial(2*j+1,k). - Andrew Howroyd, Apr 13 2021

Example

First few rows of the triangle =
1;
1, 1;
2, 3, 1;
2, 4, 3, 1;
3, 8, 9, 5, 1;
3, 9, 13, 11, 5, 1;
4, 15, 28, 31, 20, 7, 1;
4, 16, 34, 46, 40, 22, 7, 1;
5, 24, 62, 102, 110, 78, 35, 9, 1;
5, 25, 70, 130, 166, 148, 91, 37, 9, 1;
6, 35, 115, 250, 376, 400, 301, 157, 54, 11, 1;
6, 36, 125, 295, 496, 610, 553, 367, 174, 56, 11, 1;
7, 48, 191, 515, 991, 1402, 1477, 1159, 669, 276, 77, 13, 1;
7, 49, 203, 581, 1211, 1897, 2269, 2083, 1461, 771, 297, 709, 13, 1;
...

Prog

(PARI) T(n, k) = {binomial(n, k) + sum(j=0, n\2-1, binomial(2*j+1, k))} \\ Andrew Howroyd, Apr 13 2021

Crossrefs

Row sums are A061547(n+1).

Cf. A177992 = A007318 * A177990.

Cf. A061547.

Sequence in context: A233359 A279345 A097966 * A256990 A071503 A029271

Adjacent sequences: A177990 A177991 A177992 * A177994 A177995 A177996

Keyword

nonn,tabl

Author

Gary W. Adamson, May 16 2010

Extensions

Terms a(55) and beyond from Andrew Howroyd, Apr 13 2021

Status

approved