A088131 a(n) equals the square of the n-th partial sum added to twice the n-th partial sum of the squares, divided by a(n-1), for all n>=1, with a(0)=1, a(1)=1.

1, 1, 8, 29, 115, 452, 1779, 7001, 27552, 108429, 426715, 1679308, 6608803, 26008497, 102354680, 402809917, 1585231171, 6238570004, 24551470099, 96620649225, 380244026896, 1496424637485, 5889077900715, 23176067575964

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

a(n)=4a(n-1)-a(n-3) for n>3; G.f.: A(x)=(1-3x+4x^2-2x^3)/(1-4x+x^3).

Prog

(PARI) a(0)=1; a(1)=1; for(n=2, 30, a(n)=(sum(k=0, n-1, a(k))^2 + 2*sum(k=0, n-1, a(k)^2))/a(n-1))

Crossrefs

Cf. A088132.

Sequence in context: A116952 A261478 A199207 * A072264 A110527 A189946

Adjacent sequences: A088128 A088129 A088130 * A088132 A088133 A088134

Keyword

nonn

Author

Paul D. Hanna, Sep 19 2003

Status

approved