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A248027 Sum over each antidiagonal of A248017. 6
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 (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^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: A174809 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

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)