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A132920
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a(n) = n*Fibonacci(n) + binomial(n, 2).
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2
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1, 3, 9, 18, 35, 63, 112, 196, 342, 595, 1034, 1794, 3107, 5369, 9255, 15912, 27285, 46665, 79610, 135490, 230076, 389873, 659364, 1113108, 1875925, 3156543, 5303637, 8899086, 14913047, 24961635, 41734804, 69706384, 116311602, 193898719, 322961870, 537493302
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 5*a(n-1) - 8*a(n-2) + 2*a(n-3) + 6*a(n-4) - 4*a(n-5) - a(n-6) + a(n-7).
G.f.: x*(1 - 2*x + 2*x^2 - 5*x^3 + 5*x^4)/((1 - x)^3*(1 - x - x^2)^2).
(End)
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EXAMPLE
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a(4) = 18 = 3 + 4 + 5 + 6.
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PROG
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(PARI) a(n) = n*fibonacci(n) + binomial(n, 2); \\ Andrew Howroyd, Aug 10 2018
(PARI) Vec((1 - 2*x + 2*x^2 - 5*x^3 + 5*x^4)/((1 - x)^3*(1 - x - x^2)^2) + O(x^40)) \\ Andrew Howroyd, Aug 10 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Name changed and terms a(11) and beyond from Andrew Howroyd, Aug 10 2018
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STATUS
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approved
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