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

0,2

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

Table of n, a(n) for n=0..39.

Wikipedia, Cubohemioctahedron

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

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A198160 A029531 A158485 * A005902 A051798 A206372

Adjacent sequences: A274970 A274971 A274972 * A274974 A274975 A274976

Keyword

nonn,easy

Author

Steven Beard, Jul 13 2016

Status

approved