A087956 -id:A087956 - cp's OEIS frontend

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

Paul D. Hanna, Sep 16 2003

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

Cf. A087640, A087955, A087956, A087958.

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))

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).

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.

Original entry on oeis.org

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

Paul D. Hanna, Sep 16 2003

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

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

Cf. A087640, A087955, A087956, A087957.

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

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))

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).

cp's OEIS Frontend

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.

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