A100155 Structured truncated octahedral numbers.

1, 24, 103, 272, 565, 1016, 1659, 2528, 3657, 5080, 6831, 8944, 11453, 14392, 17795, 21696, 26129, 31128, 36727, 42960, 49861, 57464, 65803, 74912, 84825, 95576, 107199, 119728, 133197, 147640, 163091, 179584, 197153, 215832, 235655, 256656, 278869, 302328

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..5000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A100154, A100156 for adjacent structured Archimedean solids; A100145 for more on structured polyhedral numbers. Similar to truncated octahedral numbers A005910.

Programs

Magma

[(1/6)*(34*n^3-36*n^2+8*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {1, 24, 103, 272}, 50] (* Paolo Xausa, Aug 06 2025 *)

Formula

a(n) = (1/3)*n*(17*n^2 - 18*n + 4).

G.f.: x*(1 + 20*x + 13*x^2)/(1-x)^4. - Colin Barker, Feb 12 2012

From Elmo R. Oliveira, Aug 05 2025: (Start)

E.g.f.: exp(x)*x*(17*x^2 + 33*x + 3)/3.

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