A248027 Sum over each antidiagonal of A248017.

0, 0, 0, 4, 69, 554, 3100, 13288, 47492, 147050, 407568, 1030912, 2419025, 5324684, 11099416, 22065120, 42085344, 77378556, 137705904, 237996060, 400624581, 658434694, 1058839380, 1669118984, 2583424948, 3931632406, 5890783808, 8699293304, 12674960961

Offset

1,4

Links

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

Formula

Empirically, a(n) = (2*n^11 + 22*n^10 + 22*n^9 - 462*n^8 - 1122*n^7 + 7392*n^6 - 3509*n^5 - 25663*n^4 + 48950*n^3 - 22869*n^2 - 65133*n + 41580 - (693*n^5 + 3465*n^4 - 6930*n^3 - 45045*n^2 + 27027*n + 41580)*(-1)^n)/2661120.

Empirical g.f.: -x^4*(x^11 + 2*x^10 - 7*x^9 - 10*x^8 - 28*x^7 - 170*x^6 - 484*x^5 - 538*x^4 - 461*x^3 - 176*x^2 - 45*x - 4) / ((x - 1)^12*(x + 1)^6). - Colin Barker, Apr 21 2015

Example

a(1)..a(9) are formed as follows:
.             Antidiagonals of A248017                 n   a(n)
.                         0                             1      0
.                      0     0                          2      0
.                   0     0     0                       3      0
.                0     2     2     0                    4      4
.             1    14    39    14     1                 5     69
.          3    66   208   208    66     3              6    554
.      12   198   794  1092   794   198    12           7   3100
.   28   508  2196  3912  3912  2196   508    28        8  13288
.66  1092  5231 10626 13462 10626  5231  1092    66     9  47492

Maple

b := proc (n::integer, k::integer)::integer;
  (4*k^5*n^5 - 40*k^4*n^4 + 140*k^3*n^3 + 2*k^5 + 20*k^4*n
   + 30*k^3*n^2 + 30*k^2*n^3 + 20*k*n^4 + 2*n^5 - 40*k^4
   - 120*k^3*n - 185*k^2*n^2 - 120*k*n^3 - 40*n^4 + 160*k^3
   - 20*k^2*n - 20*k*n^2 + 160*n^3 - 80*k^2 + 36*k*n - 80*n^2
   + 48*k + 48*n + 45
   + (- 30*k^2*n^3 - 20*k*n^4 - 2*n^5 - 15*k^2*n^2 + 120*k*n^3
      + 40*n^4 + 20*k*n^2 - 160*n^3 + 60*k*n + 80*n^2 - 48*n
      - 45)*(-1)^k
   + (- 2*k^5 - 20*k^4*n - 30*k^3*n^2 + 40*k^4 + 120*k^3*n
      - 15*k^2*n^2 - 160*k^3 + 20*k^2*n + 80*k^2 + 60*k*n - 48*k
      - 45)*(-1)^n
   + (15*k^2*n^2 - 60*k*n + 45)*(-1)^k*(-1)^n)/1920;
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. A248017.

Sequence in context: A363427 A125587 A134794 * A093852 A065573 A308294

Adjacent sequences: A248024 A248025 A248026 * A248028 A248029 A248030

Keyword

nonn

Author

Christopher Hunt Gribble, Sep 30 2014

Extensions

Terms corrected and extended by Christopher Hunt Gribble, Apr 17 2015

Status

approved