A087956 a(n) is the square of the n-th partial sum minus the n-th partial sum of the squares, divided by a(n-1), for all n>=1, starting with a(0)=1, a(1)=3.

1, 3, 2, 11, 14, 45, 76, 197, 380, 895, 1838, 4143, 8762, 19353, 41496, 90793, 195928, 426811, 923802, 2008307, 4352902, 9454021, 20504420, 44513581, 96572820, 209609143, 454814022, 987068631, 2141901554, 4648293425, 10086929456

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Formula

a(n) = a(n-1) + 3*a(n-2) - a(n-3) for n>3.

G.f.: (1+2*x-4*x^2+x^3)/(1-x-3*x^2+x^3).

Example

a(4) = 14 since ((1+3+2+11)^2 - (1^2+3^2+2^2+11^2))/11 = (17^2-135)/11 = 14.

Prog

(PARI) a(0)=1; a(1)=3; for(n=2, 50, a(n)=((sum(k=0, n, a(k))^2-sum(k=0, n, a(k)^2))/a(n-1))

Crossrefs

Cf. A087640, A087955, A087957, A087958.

Essentially the same as A052973.

Sequence in context: A194608 A297870 A052973 * A116391 A305491 A358589

Adjacent sequences: A087953 A087954 A087955 * A087957 A087958 A087959

Keyword

nonn,easy

Author

Paul D. Hanna, Sep 16 2003

Status

approved