

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



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 *)


PROG



CROSSREFS

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


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



