login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A274974 Centered octahemioctahedral numbers: a(n) = (4*n^3+24*n^2+8*n+3)/3. 1

%I

%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 *)

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

%K nonn

%O 0,2

%A _Steven Beard_, Jul 13 2016

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 25 08:37 EDT 2017. Contains 287015 sequences.