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A100148
Structured small rhombicosidodecahedral numbers.
3
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
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
KEYWORD
easy,nonn
AUTHOR
James A. Record (james.record(AT)gmail.com), Nov 07 2004
STATUS
approved