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

1,2

Links

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

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

Example

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

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;

Crossrefs

Cf. A244306.

Sequence in context: A136907 A259144 A090145 * A368881 A270109 A360421

Adjacent sequences: A244304 A244305 A244306 * A244308 A244309 A244310

Keyword

nonn

Author

Christopher Hunt Gribble, Jun 25 2014

Extensions

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

Status

approved