

A274974


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


2



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
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OFFSET

0,2


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

Table of n, a(n) for n=0..40.
Steven Beard, Music track made with this sequence
Wikipedia, Octahemioctahedron


FORMULA

a(n) = (4*n^3+24*n^2+8*n+3)/3.
G.f.: (5*x^3+3*x^2+9*x+1)/(x1)^4.


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 *)


PROG

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


CROSSREFS

Cf. A005902 (centered cuboctahedral numbers), A274973 (centered cubohemioctahedral numbers).
Sequence in context: A044496 A158480 A009951 * A251142 A319086 A146287
Adjacent sequences: A274971 A274972 A274973 * A274975 A274976 A274977


KEYWORD

nonn,easy


AUTHOR

Steven Beard, Jul 13 2016


STATUS

approved



