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 A248016 Sum over each antidiagonal of A248011. 6
 0, 0, 3, 16, 67, 204, 546, 1268, 2714, 5348, 9965, 17580, 29781, 48520, 76660, 117624, 176196, 257976, 370503, 522456, 725175, 991540, 1337974, 1782924, 2349438, 3063164, 3955601, 5061524, 6423017, 8086224, 10106280, 12543280, 15468232, 18958128, 23103051, 28000224, 33762411, 40510812, 48384906, 57534052 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Christopher Hunt Gribble, Table of n, a(n) for n = 1..10000 FORMULA Empirically, a(n) = (2*n^7 + 14*n^6 + 14*n^5 + 70*n^4 - 77*n^3 - 399*n^2 + 61*n + 105 - 105*(-1)^n - 35*n^3*(-1)^n - 105*n^2*(-1)^n + 35*n*(-1)^n)/6720. Empirical g.f.: -x^3*(x^2+1)*(x^4-6*x^2-4*x-3) / ((x-1)^8*(x+1)^4). - Colin Barker, Apr 06 2015 EXAMPLE a(1..9) are formed as follows: . Antidiagonals of A248011 n a(n) . 0 1 0 . 0 0 2 0 . 1 1 1 3 3 . 2 6 6 2 4 16 . 6 14 27 14 6 5 67 . 10 32 60 60 32 10 6 204 . 19 55 129 140 129 55 19 7 546 . 28 94 218 294 294 218 94 28 8 1268 .44 140 363 506 608 506 363 140 44 9 2714 MAPLE b := proc (n::integer, k::integer)::integer; (4*k^3*n^3 - 12*k^2*n^2 + 2*k^3 + 6*k^2*n + 6*k*n^2 + 2*n^3 - 12*k^2 + 11*k*n - 12*n^2 + 4*k + 4*n - 3 - (2*k^3 + 6*k^2*n - 12*k^2 + 3*k*n + 4*k - 3)*(-1)^n - (6*k*n^2 + 2*n^3 + 3*k*n - 12*n^2 + 4*n - 3)*(-1)^k + (3*k*n - 3)*(-1)^k*(-1)^n)/96; 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. A248011. Sequence in context: A044046 A179600 A278089 * A000269 A015524 A012279 Adjacent sequences: A248013 A248014 A248015 * A248017 A248018 A248019 KEYWORD nonn AUTHOR Christopher Hunt Gribble, Sep 29 2014 EXTENSIONS Terms corrected and extended by Christopher Hunt Gribble, Apr 02 2015 STATUS approved

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Last modified December 3 21:20 EST 2023. Contains 367540 sequences. (Running on oeis4.)