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 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 (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 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 *) 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

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Last modified October 24 02:14 EDT 2018. Contains 316541 sequences. (Running on oeis4.)