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

1,2

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).

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

Maple

A100153:=n->(n*(33*n^2-41*n+10))/2; seq(A100153(k), k=1..40); # Wesley Ivan Hurt, Oct 24 2013

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 *)

Prog

(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

Crossrefs

Cf. A100152, A100154 for adjacent structured Archimedean solids; A100145 for more on structured polyhedral numbers.

Sequence in context: A075295 A189542 A134587 * A333966 A059461 A328156

Adjacent sequences: A100150 A100151 A100152 * A100154 A100155 A100156

Keyword

nonn,easy

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Status

approved