A087957 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)=4.

1, 4, 2, 14, 16, 56, 90, 242, 456, 1092, 2218, 5038, 10600, 23496, 50258, 110146, 237424, 517604, 1119730, 2435118, 5276704, 11462328, 24857322, 53967602, 117077240, 254122724, 551386842, 1196677774, 2596715576, 5635362056

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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+3*x-5*x^2+x^3)/(1-x-3*x^2+x^3).

Example

a(4) = 16 since ((1+4+2+14)^2 - (1^2+4^2+2^2+14^2))/14 = (21^2-217)/14 = 16.

Mathematica

LinearRecurrence[{1, 3, -1}, {1, 4, 2, 14}, 40] (* Harvey P. Dale, Jan 19 2026 *)

Prog

(PARI) a(0)=1; a(1)=4; 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, A087958.

Sequence in context: A184183 A317738 A224893 * A360084 A019061 A019012

Adjacent sequences: A087954 A087955 A087956 * A087958 A087959 A087960

Keyword

nonn,easy

Author

Paul D. Hanna, Sep 16 2003

Status

approved