



1, 2, 1, 3, 3, 1, 2, 6, 5, 1, 1, 5, 12, 6, 1, 2, 3, 14, 17, 8, 1, 3, 7, 14, 24, 26, 9, 1, 2, 12, 27, 30, 45, 33, 11, 1, 1, 9, 45, 62, 70, 66, 45, 12, 1, 2, 5, 44, 111, 147, 120, 104, 54, 14, 1, 3, 11, 39, 128, 273, 273, 217, 140, 69, 15, 1, 2, 18, 65, 139, 366, 546, 518, 329, 200, 80, 17, 1
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OFFSET

0,2


COMMENTS

Row sums = 1, 3, 7, 14, 25, 45, 85, ... (This is probably a new sequence and should be added to the OEIS.)  N. J. A. Sloane, Aug 09 2019


LINKS

Jinyuan Wang, Table of n, a(n) for n = 0..5150


FORMULA

A007318 + A065941  A168561 as infinite lower triangular matrices.


EXAMPLE

First few rows of the triangle are:
1,
2, 1,
3, 3, 1,
2, 6, 5, 1,
1, 5, 12, 6, 1,
2, 3, 14, 17, 8, 1,
3, 7, 14, 24, 26, 9, 1,
...


PROG

(PARI) T007318(n, k) = binomial(n, k);
T065941(n, k) = binomial(n  (k+1)\2, k\2);
T049310(n, k) = if ((n+k)%2, 0, (1)^((n+k)/2 + k) * binomial((n+k)/2, k));
T(n, k) = T007318(n, k) + T065941(n, k)  T049310(n, k); \\ Michel Marcus, Apr 28 2014


CROSSREFS

Cf. A007318, A065941, A049310, A117591, A131375, A168561.
Sequence in context: A126572 A162910 A098975 * A127121 A238703 A185908
Adjacent sequences: A309210 A309211 A309212 * A309214 A309215 A309216


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Jul 04 2007


EXTENSIONS

The old definition of A131376 did not match the data, as Michel Marcus pointed out. The definition there has been corrected, keeping the old data. The present sequence uses the old definition with corrected data from Michel Marcus.  N. J. A. Sloane, Aug 09 2019
More terms from Jinyuan Wang, Aug 29 2019


STATUS

approved



