A309213 - OEIS

%I #15 Aug 30 2019 04:14:22

%S 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,

%T 27,30,45,33,11,1,1,9,45,62,70,66,45,12,1,2,5,44,111,147,120,104,54,

%U 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

%N A007318 + A065941 - A049310.

%C 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

%H Jinyuan Wang, <a href="/A309213/b309213.txt">Table of n, a(n) for n = 0..5150</a>

%F A007318 + A065941 - A168561 as infinite lower triangular matrices.

%e First few rows of the triangle are:

%e 1,

%e 2, 1,

%e 3, 3, 1,

%e 2, 6, 5, 1,

%e 1, 5, 12, 6, 1,

%e 2, 3, 14, 17, 8, 1,

%e 3, 7, 14, 24, 26, 9, 1,

%e ...

%o (PARI) T007318(n, k) = binomial(n, k);

%o T065941(n, k) = binomial(n - (k+1)\2, k\2);

%o T049310(n, k) = if ((n+k)%2, 0, (-1)^((n+k)/2 + k) * binomial((n+k)/2, k));

%o T(n, k) = T007318(n, k) + T065941(n, k) - T049310(n, k); \\ _Michel Marcus_, Apr 28 2014

%Y Cf. A007318, A065941, A049310, A117591, A131375, A168561.

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_, Jul 04 2007

%E 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

%E More terms from _Jinyuan Wang_, Aug 29 2019