A244307 Sum over each antidiagonal of A244306.

0, 2, 7, 20, 45, 92, 170, 296, 486, 766, 1161, 1708, 2443, 3416, 4676, 6288, 8316, 10842, 13947, 17732, 22297, 27764, 34254, 41912, 50882, 61334, 73437, 87388, 103383, 121648, 142408, 165920, 192440, 222258, 255663, 292980, 334533, 380684, 431794, 488264

Offset: 1

Author

Christopher Hunt Gribble, Jun 25 2014

Keywords

• nonn

Examples

			a(1..9) are formed as follows:
.        Antidiagonals of A244306             n  a(n)
.                    0                        1     0
.                  1   1                      2     2
.                2   3   2                    3     7
.              4   6   6   4                  4    20
.            6  10  13  10   6                5    45
.          9  15  22  22  15   9              6    92
.       12  21  34  36  34  21  12            7   170
.     16  28  48  56  56  48  28  16          8   296
.   20  36  65  78  88  78  65  36  20        9   486
		

Links

• Christopher Hunt Gribble, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A244306.

Programs

Maple

b := proc (n::integer, k::integer)::integer;
(4*k^2*n^2 + 2*k^2 + 8*k*n + 2*n^2 - 4*k - 4*n - 1 -
(2*k^2 - 4*k - 1)*(-1)^n - (2*n^2 - 4*n - 1)*(-1)^k -
(-1)^k*(-1)^n)*(1/32);
end proc;
for j to 40 do
   a := 0;
   for k from j by -1 to 1 do
      n := j - k + 1;
      a := a + b(n, k);
   end do;
   printf("%d, ", a);
end do;

Formula

Empirically, a(n) = (6*n^5 + 30*n^4 + 180*n^3 + 240*n^2 - 141*n - 135 + (45*n + 135)*(-1)^n)/1440.

Empirical g.f.: x^2*(x^3-x+2) / ((x-1)^6*(x+1)^2). - Colin Barker, Jun 01 2015

Extensions

Terms corrected and extended by Christopher Hunt Gribble, Mar 31 2015