A274974 - OEIS

%I #38 Nov 03 2017 09:48:58

%S 1,13,49,117,225,381,593,869,1217,1645,2161,2773,3489,4317,5265,6341,

%T 7553,8909,10417,12085,13921,15933,18129,20517,23105,25901,28913,

%U 32149,35617,39325,43281,47493,51969,56717,61745,67061,72673,78589,84817,91365,98241

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

%C 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.

%H Steven Beard, <a href="https://oeis.org/w/images/c/c5/A274974_Beard.mp3">Music track made with this sequence</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Octahemioctahedron">Octahemioctahedron</a>

%F a(n) = (4*n^3+24*n^2+8*n+3)/3.

%F G.f.: (-5*x^3+3*x^2+9*x+1)/(x-1)^4.

%t CoefficientList[Series[(-5 x^3 + 3 x^2 + 9 x + 1)/(x - 1)^4, {x, 0, 40}], x] (* or *)

%t Table[(4 n^3 + 24 n^2 + 8 n+3)/3, {n, 41}] (* _Michael De Vlieger_, Jul 13 2016 *)

%o (PARI) a(n)=(4*n^3+24*n^2+8*n+3)/3 \\ _Charles R Greathouse IV_, Nov 03 2017

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

%K nonn,easy

%O 0,2

%A _Steven Beard_, Jul 13 2016