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

1,2

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).

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)

Prog

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

Crossrefs

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

Sequence in context: A084195 A033856 A143861 * A372675 A120371 A062022

Adjacent sequences: A100171 A100172 A100173 * A100175 A100176 A100177

Keyword

easy,nonn

Author

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

Extensions

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

Status

approved