A115294 Diagonal sums of correlation triangle for (1+x)^3/(1-x).

1, 4, 11, 25, 47, 79, 122, 175, 239, 314, 399, 495, 602, 719, 847, 986, 1135, 1295, 1466, 1647, 1839, 2042, 2255, 2479, 2714, 2959, 3215, 3482, 3759, 4047, 4346, 4655, 4975, 5306, 5647, 5999, 6362, 6735, 7119, 7514, 7919, 8335, 8762, 9199, 9647, 10106

Offset: 0

Author

Paul Barry, Jan 19 2006

Keywords

• easy
• nonn

Comments

Diagonal sums of number triangle A115292.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Programs

Mathematica

LinearRecurrence[{2,-1,1,-2,1},{1,4,11,25,47,79,122,175,239},50] (* Harvey P. Dale, Jun 11 2017 *)

Formula

G.f.: (1+x)^2*(1+x^2)^3/((1-x)^2*(1-x^3)); a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, [j<=k]*A115291(k-j)*[j<=n-2k]*A115291(n-2k-j)}}.