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A274974 Centered octahemioctahedral numbers: a(n) = (4*n^3+24*n^2+8*n+3)/3. 1
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 (list; graph; refs; listen; history; text; internal format)
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)/(x-1)^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 *)

CROSSREFS

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

Sequence in context: A044496 A158480 A009951 * A251142 A146287 A147346

Adjacent sequences:  A274971 A274972 A274973 * A274975 A274976 A274977

KEYWORD

nonn

AUTHOR

Steven Beard, Jul 13 2016

STATUS

approved

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Last modified May 23 14:46 EDT 2017. Contains 286925 sequences.