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Search: id:A087957
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| A087957 |
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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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+0
3
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| 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
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OFFSET
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0,2
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FORMULA
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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).
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EXAMPLE
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a(4)=16 since ((1+4+2+14)^2 - (1^2+4^2+2^2+14^2))/14 = (21^2-217)/14 = 16.
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PROGRAM
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(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))
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CROSSREFS
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Cf. A087640, A087955, A087956, A087958.
Sequence in context: A096034 A064308 A161134 this_sequence A019012 A019061 A154333
Adjacent sequences: A087954 A087955 A087956 this_sequence A087958 A087959 A087960
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Sep 16 2003
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