A087958 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)=5.

1, 5, 2, 17, 18, 67, 104, 287, 532, 1289, 2598, 5933, 12438, 27639, 59020, 129499, 278920, 608397, 1315658, 2861929, 6200506, 13470635, 29210224, 63421623, 137581660, 298636305, 647959662, 1406286917, 3051529598, 6622430687

Offset

0,2

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (1,3,-1).

Formula

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

G.f.: (1+4*x-6*x^2+x^3)/(1-x-3*x^2+x^3).

Example

a(4) = 18 since ((1+5+2+17)^2 - (1^2+5^2+2^2+17^2))/17 = (25^2-319)/17 = 18.

Mathematica

Join[{1}, LinearRecurrence[{1, 3, -1}, {5, 2, 17}, 30]] (* Harvey P. Dale, Jul 07 2011 *)

Prog

(PARI) a(0)=1; a(1)=5; 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, A087956, A087957.

Sequence in context: A146343 A146363 A246797 * A286161 A286252 A286154

Adjacent sequences: A087955 A087956 A087957 * A087959 A087960 A087961

Keyword

nonn,easy

Author

Paul D. Hanna, Sep 16 2003

Status

approved