A100164 Structured rhombic triacontahedral numbers (vertex structure 11).

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

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 A363531 A224041

Adjacent sequences: A100161 A100162 A100163 * A100165 A100166 A100167

Keyword

easy,nonn

Author

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

Status

approved