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A053808
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Partial sums of A001891.
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12
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1, 5, 15, 36, 76, 148, 273, 485, 839, 1424, 2384, 3952, 6505, 10653, 17383, 28292, 45964, 74580, 120905, 195885, 317231, 513600, 831360, 1345536, 2177521, 3523733, 5701983, 9226500, 14929324, 24156724, 39087009, 63244757, 102332855, 165578768, 267912848
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OFFSET
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0,2
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COMMENTS
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Also number CG(n,2) of complete games with n players of 2 types. - N. J. A. Sloane, Dec 29 2012
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-2) + (n+1)^2, a(-n)=0.
G.f.: (1+x)/((1-x-x^2)*(1-x)^3).
a(n) = Fibonacci(n+6) - (n^2 + 4*n + 8), n >= 2 (see p. 184 of FQ reference).
a(n-2) = Sum_{i=0..n} Fibonacci(i)*(n-i)^2. - Benoit Cloitre, Mar 06 2004
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MATHEMATICA
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Table[Fibonacci[n+8] -(n^2 +8*n+20), {n, 0, 40}] (* G. C. Greubel, Jul 06 2019 *)
LinearRecurrence[{4, -5, 1, 2, -1}, {1, 5, 15, 36, 76}, 40] (* Harvey P. Dale, Apr 14 2022 *)
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PROG
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(PARI) vector(40, n, n--; fibonacci(n+8) - (n^2 +8*n+20)) \\ G. C. Greubel, Jul 06 2019
(Magma) [Fibonacci(n+8) - (n^2+8*n+20): n in [0..40]]; // G. C. Greubel, Jul 06 2019
(Sage) [fibonacci(n+8) - (n^2 +8*n+20) for n in (0..20)] # G. C. Greubel, Jul 06 2019
(GAP) List([0..40], n-> Fibonacci(n+8) - (n^2 +8*n+20)) # G. C. Greubel, Jul 06 2019
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CROSSREFS
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Right-hand column 7 of triangle A011794.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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