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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

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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