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A244307
Sum over each antidiagonal of A244306.
6
0, 2, 7, 20, 45, 92, 170, 296, 486, 766, 1161, 1708, 2443, 3416, 4676, 6288, 8316, 10842, 13947, 17732, 22297, 27764, 34254, 41912, 50882, 61334, 73437, 87388, 103383, 121648, 142408, 165920, 192440, 222258, 255663, 292980, 334533, 380684, 431794, 488264
OFFSET
1,2
LINKS
Christopher Hunt Gribble, Table of n, a(n) for n = 1..10000
FORMULA
Empirically, a(n) = (6*n^5 + 30*n^4 + 180*n^3 + 240*n^2 - 141*n - 135 + (45*n + 135)*(-1)^n)/1440.
Empirical g.f.: x^2*(x^3-x+2) / ((x-1)^6*(x+1)^2). - Colin Barker, Jun 01 2015
EXAMPLE
a(1..9) are formed as follows:
. Antidiagonals of A244306 n a(n)
. 0 1 0
. 1 1 2 2
. 2 3 2 3 7
. 4 6 6 4 4 20
. 6 10 13 10 6 5 45
. 9 15 22 22 15 9 6 92
. 12 21 34 36 34 21 12 7 170
. 16 28 48 56 56 48 28 16 8 296
. 20 36 65 78 88 78 65 36 20 9 486
MAPLE
b := proc (n::integer, k::integer)::integer;
(4*k^2*n^2 + 2*k^2 + 8*k*n + 2*n^2 - 4*k - 4*n - 1 -
(2*k^2 - 4*k - 1)*(-1)^n - (2*n^2 - 4*n - 1)*(-1)^k -
(-1)^k*(-1)^n)*(1/32);
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. A244306.
Sequence in context: A136907 A259144 A090145 * A368881 A270109 A360421
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms corrected and extended by Christopher Hunt Gribble, Mar 31 2015
STATUS
approved