A100148 Structured small rhombicosidodecahedral numbers.

1, 60, 285, 784, 1665, 3036, 5005, 7680, 11169, 15580, 21021, 27600, 35425, 44604, 55245, 67456, 81345, 97020, 114589, 134160, 155841, 179740, 205965, 234624, 265825, 299676, 336285, 375760, 418209, 463740, 512461, 564480

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) = (1/6)*(108*n^3 - 150*n^2 + 48*n).

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)=285, a(4)=784. - Harvey P. Dale, Oct 10 2011

G.f.: x*(x*(51*x+56)+1)/(x-1)^4. - Harvey P. Dale, Oct 10 2011

E.g.f.: x*(1 + 29*x + 18*x^2)*exp(x). - G. C. Greubel, Oct 18 2018

Mathematica

Table[(108n^3-150n^2+48n)/6, {n, 40}] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {1, 60, 285, 784}, 40](* Harvey P. Dale, Oct 10 2011 *)

Prog

(Magma) [(1/6)*(108*n^3-150*n^2+48*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011
(PARI) vector(50, n, (108*n^3 - 150*n^2 + 48*n)/6) \\ G. C. Greubel, Oct 18 2018

Crossrefs

Cf. A100147, A100149 for adjacent structured Archimedean solids; and A100145 for more on structured polyhedral numbers.

Sequence in context: A160917 A100154 A246230 * A100151 A338109 A179811

Adjacent sequences: A100145 A100146 A100147 * A100149 A100150 A100151

Keyword

easy,nonn

Author

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

Status

approved