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A248016 Sum over each antidiagonal of A248011.

%I A248016 #23 Nov 30 2016 22:12:33
%S A248016 0,0,3,16,67,204,546,1268,2714,5348,9965,17580,29781,48520,76660,
%T A248016 117624,176196,257976,370503,522456,725175,991540,1337974,1782924,
%U A248016 2349438,3063164,3955601,5061524,6423017,8086224,10106280,12543280,15468232,18958128,23103051,28000224,33762411,40510812,48384906,57534052
%N A248016 Sum over each antidiagonal of A248011.
%H A248016 Christopher Hunt Gribble, <a href="/A248016/b248016.txt">Table of n, a(n) for n = 1..10000</a>
%F A248016 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.
%F A248016 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
%e A248016 a(1..9) are formed as follows:
%e A248016 .             Antidiagonals of A248011                n  a(n)
%e A248016 .                         0                            1     0
%e A248016 .                      0     0                         2     0
%e A248016 .                   1     1     1                      3     3
%e A248016 .                2     6     6     2                   4    16
%e A248016 .             6    14    27    14     6                5    67
%e A248016 .         10    32    60    60    32    10             6   204
%e A248016 .      19    55   129   140   129    55    19          7   546
%e A248016 .   28    94   218   294   294   218    94    28       8  1268
%e A248016 .44   140   363   506   608   506   363   140    44    9  2714
%p A248016 b := proc (n::integer, k::integer)::integer;
%p A248016 (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;
%p A248016 end proc;
%p A248016 for j to 10000 do
%p A248016     a := 0;
%p A248016     for k from j by -1 to 1 do
%p A248016        n := j-k+1;
%p A248016        a := a+b(n, k)
%p A248016     end do;
%p A248016     printf("%d, ", a)
%p A248016 end do;
%Y A248016 Cf. A248011.
%K A248016 nonn
%O A248016 1,3
%A A248016 _Christopher Hunt Gribble_, Sep 29 2014
%E A248016 Terms corrected and extended by _Christopher Hunt Gribble_, Apr 02 2015