A274973 Centered cubohemioctahedral numbers: a(n) = 2*n^3+9*n^2+n+1.

1, 13, 55, 139, 277, 481, 763, 1135, 1609, 2197, 2911, 3763, 4765, 5929, 7267, 8791, 10513, 12445, 14599, 16987, 19621, 22513, 25675, 29119, 32857, 36901, 41263, 45955, 50989, 56377, 62131, 68263, 74785, 81709, 89047, 96811, 105013, 113665, 122779, 132367

Offset: 0

Author

Steven Beard, Jul 13 2016

Keywords

• nonn
• easy

Comments

A faceting of the cuboctahedron, sharing the same square faces. The cubohemioctahedron has the same edge and vertex arrangement as the cuboctahedron. Beginning with the fourth term, the eight tetrahedral faces are each now "missing" a tetrahedron of size 1,4,10,20,35...(A000292). See A274974 centered octahemioctahedron for similar cuboctahedral faceting but with the square faces "missing."

Links

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

Crossrefs

Cf. A005902 (centered cuboctahedral numbers), A274974 (centered octahemioctahedral numbers).

Programs

Mathematica

Table[2 n^3 + 9 n^2 + n + 1, {n, 40}] (* Michael De Vlieger, Jul 13 2016 *)
LinearRecurrence[{4,-6,4,-1},{1,13,55,139},40] (* Harvey P. Dale, Feb 18 2024 *)

PARI

a(n)=2*n^3+9*n^2+n+1 \\ Charles R Greathouse IV, Jul 14 2016

Formula

a(n) = 2*n^3+9*n^2+n+1.

G.f.: (-7*x^3+9*x^2+9*x+1)/(x-1)^4.