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

Author

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

Keywords

• easy
• nonn

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

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

Programs

Magma

[(1/6)*(108*n^3-150*n^2+48*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011

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 *)

PARI

vector(50, n, (108*n^3 - 150*n^2 + 48*n)/6) \\ G. C. Greubel, Oct 18 2018

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