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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.)