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A100183
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Structured hexagonal anti-prism numbers.
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1
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1, 12, 46, 116, 235, 416, 672, 1016, 1461, 2020, 2706, 3532, 4511, 5656, 6980, 8496, 10217, 12156, 14326, 16740, 19411, 22352, 25576, 29096, 32925, 37076, 41562, 46396, 51591, 57160, 63116, 69472
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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) = (1/6)*(13*n^3 - 9*n^2 + 2*n). [Corrected by Luca Colucci, Mar 01 2011]
G.f.: x*(1 + 8*x + 4*x^2)/(1-x)^4. - Colin Barker, Jun 08 2012
E.g.f.: (6*x +30*x^2 +13*x^3)*exp(x)/6. - G. C. Greubel, Nov 08 2018
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MATHEMATICA
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Table[(13*n^3 - 9*n^2 + 2*n)/6, {n, 1, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 12, 46, 116}, 40] (* G. C. Greubel, Nov 08 2018 *)
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PROG
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(PARI) vector(40, n, (13*n^3 - 9*n^2 + 2*n)/6) \\ G. C. Greubel, Nov 08 2018
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CROSSREFS
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Cf. A100185 - structured anti-prisms; A100145 for more on structured numbers.
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KEYWORD
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easy,nonn
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AUTHOR
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James A. Record (james.record(AT)gmail.com), Nov 07 2004
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STATUS
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approved
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