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%I #26 Nov 30 2016 22:17:30
%S 0,2,7,20,45,92,170,296,486,766,1161,1708,2443,3416,4676,6288,8316,
%T 10842,13947,17732,22297,27764,34254,41912,50882,61334,73437,87388,
%U 103383,121648,142408,165920,192440,222258,255663,292980,334533,380684,431794,488264
%N Sum over each antidiagonal of A244306.
%H Christopher Hunt Gribble, <a href="/A244307/b244307.txt">Table of n, a(n) for n = 1..10000</a>
%F Empirically, a(n) = (6*n^5 + 30*n^4 + 180*n^3 + 240*n^2 - 141*n - 135 + (45*n + 135)*(-1)^n)/1440.
%F Empirical g.f.: x^2*(x^3-x+2) / ((x-1)^6*(x+1)^2). - _Colin Barker_, Jun 01 2015
%e a(1..9) are formed as follows:
%e . Antidiagonals of A244306 n a(n)
%e . 0 1 0
%e . 1 1 2 2
%e . 2 3 2 3 7
%e . 4 6 6 4 4 20
%e . 6 10 13 10 6 5 45
%e . 9 15 22 22 15 9 6 92
%e . 12 21 34 36 34 21 12 7 170
%e . 16 28 48 56 56 48 28 16 8 296
%e . 20 36 65 78 88 78 65 36 20 9 486
%p b := proc (n::integer, k::integer)::integer;
%p (4*k^2*n^2 + 2*k^2 + 8*k*n + 2*n^2 - 4*k - 4*n - 1 -
%p (2*k^2 - 4*k - 1)*(-1)^n - (2*n^2 - 4*n - 1)*(-1)^k -
%p (-1)^k*(-1)^n)*(1/32);
%p end proc;
%p for j to 40 do
%p a := 0;
%p for k from j by -1 to 1 do
%p n := j - k + 1;
%p a := a + b(n, k);
%p end do;
%p printf("%d, ", a);
%p end do;
%Y Cf. A244306.
%K nonn
%O 1,2
%A _Christopher Hunt Gribble_, Jun 25 2014
%E Terms corrected and extended by _Christopher Hunt Gribble_, Mar 31 2015
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