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A100147
Structured icosidodecahedral numbers.
7
1, 30, 135, 364, 765, 1386, 2275, 3480, 5049, 7030, 9471, 12420, 15925, 20034, 24795, 30256, 36465, 43470, 51319, 60060, 69741, 80410, 92115, 104904, 118825, 133926, 150255, 167860, 186789, 207090, 228811, 252000, 276705, 302974, 330855, 360396, 391645, 424650
OFFSET
1,2
COMMENTS
Equals row sums of triangle A143254 & binomial transform of [1, 29, 76, 48, 0, 0, 0, ...]. - Gary W. Adamson, Aug 02 2008
Apart from offset, same as A079588.
FORMULA
a(n) = (1/6)*(48*n^3 - 60*n^2 + 18*n).
a(n) = A079588(n-1) = n*(2*n-1)*(4*n-3). - R. J. Mathar, Sep 02 2008
From Jaume Oliver Lafont, Sep 08 2009: (Start)
a(n) = (1+(n-1))*(1+2*(n-1))*(1+4*(n-1)).
G.f.: x*(1 + 26*x + 21*x^2)/(1-x)^4. (End)
E.g.f.: x*(1 + 14*x + 8*x^2)*exp(x). - G. C. Greubel, Oct 18 2018
From Amiram Eldar, Sep 20 2022: (Start)
Sum_{n>=1} 1/a(n) = Pi/3.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*sqrt(2)*log(sqrt(2)+1)/3 + log(2)/3 - (3 - 2*sqrt(2))*Pi/6. (End)
MATHEMATICA
Table[(48*n^3 - 60*n^2 + 18*n)/6, {n, 1, 50}] (* G. C. Greubel, Oct 18 2018 *)
PROG
(Magma) [(1+(n-1))*(1+2*(n-1))*(1+4*(n-1)): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011
(PARI) a(n)=n*(8*n^2-10*n+3) \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Cf. A100146, A100148 for adjacent structured Archimedean solids; and A100145 for more on structured polyhedral numbers.
Cf. also A079588.
Sequence in context: A221522 A291582 A079588 * A117750 A348828 A158462
KEYWORD
easy,nonn
AUTHOR
James A. Record (james.record(AT)gmail.com), Nov 07 2004
STATUS
approved