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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 (list; graph; refs; listen; history; text; internal format)
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 * A270109 A123203 A309298

Adjacent sequences: A244304 A244305 A244306 * A244308 A244309 A244310

KEYWORD

nonn

AUTHOR

Christopher Hunt Gribble, Jun 25 2014

EXTENSIONS

Terms corrected and extended by Christopher Hunt Gribble, Mar 31 2015

STATUS

approved

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Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)