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A100164 Structured rhombic triacontahedral numbers (vertex structure 11). 3
1, 32, 143, 384, 805, 1456, 2387, 3648, 5289, 7360, 9911, 12992, 16653, 20944, 25915, 31616, 38097, 45408, 53599, 62720, 72821, 83952, 96163, 109504, 124025, 139776, 156807, 175168, 194909, 216080, 238731, 262912, 288673, 316064, 345135, 375936, 408517, 442928 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also structured triakis icosahedral numbers (vertex structure 11) (cf. A100172 = alternate vertex).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

FORMULA

a(n) = (1/6)*(50*n^3 - 60*n^2 + 16*n) = (1/3)*n*(5*n-2)*(5*n-4).

From Jaume Oliver Lafont, Sep 08 2009: (Start)

a(n) = (5*(n-1) + 1)*(5*(n-1) + 3)*(5*(n-1) + 5)/15.

G.f.: x*(1 + 28*x + 21*x^2)/(1-x)^4. (End)

Sum_{n>=1} 1/a(n) = 3*sqrt((25-2*sqrt(5))/5)*Pi/16 + 9*sqrt(5)*log(phi)/16 - 15*log(5)/32, where phi is the golden ratio (A001622). - Amiram Eldar, Sep 20 2022

MATHEMATICA

a[n_] := (n*(5*n - 2)*(5*n - 4))/3; Array[a, 30] (* Amiram Eldar, Sep 20 2022 *)

PROG

(Magma) [(1/6)*(50*n^3-60*n^2+16*n): n in [1..40]]; // Vincenzo Librandi, Jul 25 2011

CROSSREFS

Cf. A100165 (alternate vertex), A100145 for more on structured polyhedral numbers.

Cf. A001622, A100172.

Sequence in context: A137740 A221597 A159763 * A048191 A224041 A188839

Adjacent sequences:  A100161 A100162 A100163 * A100165 A100166 A100167

KEYWORD

easy,nonn,changed

AUTHOR

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

STATUS

approved

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Last modified September 30 21:21 EDT 2022. Contains 357106 sequences. (Running on oeis4.)