A100174 Structured tetrakis hexahedral numbers (vertex structure 5).

1, 14, 59, 156, 325, 586, 959, 1464, 2121, 2950, 3971, 5204, 6669, 8386, 10375, 12656, 15249, 18174, 21451, 25100, 29141, 33594, 38479, 43816, 49625, 55926, 62739, 70084, 77981, 86450, 95511, 105184, 115489, 126446, 138075, 150396, 163429, 177194, 191711, 207000

Offset: 1

Author

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

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A005915 = alternate vertex; cf. A100145 for more on structured numbers.

Programs

Magma

[(1/6)*(20*n^3-24*n^2+10*n): n in [1..50] ]; // Vincenzo Librandi, Aug 02 2011

Formula

a(n) = (1/6)*(20*n^3 - 24*n^2 + 10*n).

G.f.: x*(1+x)*(1+9*x)/(1-x)^4. - Colin Barker, May 29 2012

From Elmo R. Oliveira, Aug 04 2025: (Start)

E.g.f.: exp(x)*x*(10*x^2 + 18*x + 3)/3.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End)

Extensions

Formula corrected by Helena Verrill (verrill(AT)math.lsu.edu), Mar 23 2007