A274974 Centered octahemioctahedral numbers: a(n) = (4*n^3+24*n^2+8*n+3)/3.

1, 13, 49, 117, 225, 381, 593, 869, 1217, 1645, 2161, 2773, 3489, 4317, 5265, 6341, 7553, 8909, 10417, 12085, 13921, 15933, 18129, 20517, 23105, 25901, 28913, 32149, 35617, 39325, 43281, 47493, 51969, 56717, 61745, 67061, 72673, 78589, 84817, 91365, 98241

Offset: 0

Author

Steven Beard, Jul 13 2016

Keywords

• nonn
• easy

Comments

Related to a faceting of the cuboctahedron, sharing the same triangular faces. The octahemioctahedron has the same edge and vertex arrangement as the cuboctahedron (as does A274973). Beginning with the third term, the six square faces are each now "missing" a square pyramid of size 1, 5, 14, 30, 55, 91...(A000330). See A274973 centered cubohemioctahedron for similar cuboctahedral faceting but without the triangular faces.

Links

• Steven Beard, Music track made with this sequence
• Wikipedia, Octahemioctahedron

Crossrefs

Cf. A005902 (centered cuboctahedral numbers), A274973 (centered cubohemioctahedral numbers).

Programs

Mathematica

CoefficientList[Series[(-5 x^3 + 3 x^2 + 9 x + 1)/(x - 1)^4, {x, 0, 40}], x] (* or *)
Table[(4 n^3 + 24 n^2 + 8 n+3)/3, {n, 41}] (* Michael De Vlieger, Jul 13 2016 *)

PARI

a(n)=(4*n^3+24*n^2+8*n+3)/3 \\ Charles R Greathouse IV, Nov 03 2017

Formula

a(n) = (4*n^3+24*n^2+8*n+3)/3.

G.f.: (-5*x^3+3*x^2+9*x+1)/(x-1)^4.