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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = a(n-1) + 3a(n-2) - a(n-3) for n>3; G.f.: (1+3x-5x^2+x^3)/(1-x-3x^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.
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
Sequence in context: A184183 A317738 A224893 * A360084 A019061 A019012
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 16 2003
STATUS
approved

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Last modified April 16 18:22 EDT 2024. Contains 371750 sequences. (Running on oeis4.)