A248060 Sums over successive antidiagonals of A248059.

0, 0, 1, 14, 89, 416, 1526, 4740, 12898, 31680, 71527, 150722, 299571, 566592, 1026524, 1791528, 3025188, 4961280, 7926621, 12370710, 18901069, 28327904, 41716466, 60451820, 86313734, 121567680, 169068835, 232386570, 315945319, 425191040, 566777976, 748786896

Offset

1,4

Links

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

Formula

Empirically, a(n) = (2*n^9 + 18*n^8 + 18*n^7 - 210*n^6 + 588*n^5 + 672*n^4 - 3803*n^3 - 1425*n^2 + 3195*n + 945 + 315*n^3*(-1)^n + 945*n^2*(-1)^n - 315*n*(-1)^n - 945*(-1)^n)/120960.

Empirical g.f.: x^3*(x^8-4*x^6+8*x^5+26*x^4+40*x^3+16*x^2+8*x+1) / ((x-1)^10*(x+1)^4). - Colin Barker, Apr 08 2015

Example

a(1..9) are formed as follows:
.             Antidiagonals of A248059                   n    a(n)
.                         0                              1       0
.                      0     0                           2       0
.                   0     1     0                        3       1
.                1     6     6     1                     4      14
.             3    22    39    22     3                  5      89
.          9    60   139   139    60     9               6     416
.      19   135   371   476   371   135    19            7    1526
.   38   266   813  1253  1253   813   266    38         8    4740
.66   476  1574  2706  3254  2706  1574   476    66      9   12898

Maple

b := proc (n::integer, k::integer)::integer;
  (4*k^4*n^4 - 24*k^3*n^3 + 2*k^4 + 12*k^3*n + 80*k^2*n^2 +
   12*k*n^3 + 2*n^4 - 24*k^3 - 24*k^2*n - 24*k*n^2 - 24*n^3 +
   40*k^2 - 102*k*n + 40*n^2 + 9 + (- 2*k^4 - 12*k^3*n + 24*k^3 +
   24*k^2*n - 40*k^2 + 6*k*n - 9)*(-1)^n + (- 12*k*n^3 - 2*n^4 +
   24*k*n^2 + 24*n^3 + 6*k*n - 40*n^2 - 9)*(-1)^k +
   (- 6*k*n + 9)*(-1)^k*(-1)^n)/384
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. A248059.

Sequence in context: A202785 A255535 A034544 * A186257 A241305 A195267

Adjacent sequences: A248057 A248058 A248059 * A248061 A248062 A248063

Keyword

nonn

Author

Christopher Hunt Gribble, Sep 30 2014

Extensions

Terms corrected and extended by Christopher Hunt Gribble, Apr 06 2015

Status

approved