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A100153 Structured truncated dodecahedral numbers. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 26 09:38 EST 2021. Contains 340435 sequences. (Running on oeis4.)