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A087958
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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)=5.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n) = a(n-1) + 3a(n-2) - a(n-3) for n>3; G.f.: (1+4x-6x^2+x^3)/(1-x-3x^2+x^3).
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EXAMPLE
| a(4)=18 since ((1+5+2+17)^2 - (1^2+5^2+2^2+17^2))/17 = (25^2-217)/17 = 18.
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MATHEMATICA
| Join[{1}, LinearRecurrence[{1, 3, -1}, {5, 2, 17}, 30]] (* From Harvey P. Dale, Jul 07 2011 *)
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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))
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CROSSREFS
| Cf. A087640, A087955, A087956, A087957.
Sequence in context: A111267 A146343 A146363 * A189746 A191667 A130329
Adjacent sequences: A087955 A087956 A087957 * A087959 A087960 A087961
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Sep 16 2003
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