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