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A100153
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Structured truncated dodecahedral numbers.
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3
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1, 60, 276, 748, 1575, 2856, 4690, 7176, 10413, 14500, 19536, 25620, 32851, 41328, 51150, 62416, 75225, 89676, 105868, 123900, 143871, 165880, 190026, 216408, 245125, 276276, 309960, 346276, 385323, 427200, 472006, 519840
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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) = (1/2)*n*(33*n^2 - 41*n + 10).
G.f.: x*(1 + 56*x + 42*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=1, a(2)=60, a(3)=276, a(4)=748. - Harvey P. Dale, Dec 09 2012
E.g.f.: x*(2 + 58*x + 33*x^2)*exp(x)/2. - G. C. Greubel, Oct 18 2018
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MAPLE
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MATHEMATICA
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Table[(n(33n^2-41n+10))/2, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 60, 276, 748}, 40] (* Harvey P. Dale, Dec 09 2012 *)
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PROG
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(Magma) [(1/6)*(99*n^3-123*n^2+30*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011
(PARI) vector(50, n, n*(33*n^2 - 41*n + 10)/2) \\ G. C. Greubel, Oct 18 2018
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CROSSREFS
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Cf. A100152, A100154 for adjacent structured Archimedean solids; A100145 for more on structured polyhedral numbers.
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KEYWORD
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nonn,easy
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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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