A100153 Structured truncated dodecahedral numbers.
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
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..5000
- Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).
Crossrefs
Programs
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Magma
[(1/6)*(99*n^3-123*n^2+30*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011
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Maple
A100153:=n->(n*(33*n^2-41*n+10))/2; seq(A100153(k), k=1..40); # Wesley Ivan Hurt, Oct 24 2013
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Mathematica
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 *) -
PARI
vector(50, n, n*(33*n^2 - 41*n + 10)/2) \\ G. C. Greubel, Oct 18 2018
Formula
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