A244307 - OEIS

%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