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A248060 Sums over successive antidiagonals of A248059. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 16:42 EST 2019. Contains 329879 sequences. (Running on oeis4.)