A248016 Sum over each antidiagonal of A248011.

0, 0, 3, 16, 67, 204, 546, 1268, 2714, 5348, 9965, 17580, 29781, 48520, 76660, 117624, 176196, 257976, 370503, 522456, 725175, 991540, 1337974, 1782924, 2349438, 3063164, 3955601, 5061524, 6423017, 8086224, 10106280, 12543280, 15468232, 18958128, 23103051, 28000224, 33762411, 40510812, 48384906, 57534052

Offset: 1

Author

Christopher Hunt Gribble, Sep 29 2014

Keywords

• nonn

Examples

			a(1..9) are formed as follows:
.             Antidiagonals of A248011                n  a(n)
.                         0                            1     0
.                      0     0                         2     0
.                   1     1     1                      3     3
.                2     6     6     2                   4    16
.             6    14    27    14     6                5    67
.         10    32    60    60    32    10             6   204
.      19    55   129   140   129    55    19          7   546
.   28    94   218   294   294   218    94    28       8  1268
.44   140   363   506   608   506   363   140    44    9  2714
		

Links

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

Crossrefs

Cf. A248011.

Programs

Maple

b := proc (n::integer, k::integer)::integer;
(4*k^3*n^3 - 12*k^2*n^2 + 2*k^3 + 6*k^2*n + 6*k*n^2 + 2*n^3 - 12*k^2 + 11*k*n - 12*n^2 + 4*k + 4*n - 3 - (2*k^3 + 6*k^2*n - 12*k^2 + 3*k*n + 4*k - 3)*(-1)^n - (6*k*n^2 + 2*n^3 + 3*k*n - 12*n^2 + 4*n - 3)*(-1)^k + (3*k*n - 3)*(-1)^k*(-1)^n)/96;
end proc;
for j to 10000 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) = (2*n^7 + 14*n^6 + 14*n^5 + 70*n^4 - 77*n^3 - 399*n^2 + 61*n + 105 - 105*(-1)^n - 35*n^3*(-1)^n - 105*n^2*(-1)^n + 35*n*(-1)^n)/6720.

Empirical g.f.: -x^3*(x^2+1)*(x^4-6*x^2-4*x-3) / ((x-1)^8*(x+1)^4). - Colin Barker, Apr 06 2015

Extensions

Terms corrected and extended by Christopher Hunt Gribble, Apr 02 2015