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

1,3

Links

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

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

Example

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

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;

Crossrefs

Cf. A248011.

Sequence in context: A044046 A179600 A278089 * A000269 A015524 A012279

Adjacent sequences: A248013 A248014 A248015 * A248017 A248018 A248019

Keyword

nonn

Author

Christopher Hunt Gribble, Sep 29 2014

Extensions

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

Status

approved