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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A193251 Small rhombicosidodecahedron with faces of centered polygons. 1
1, 123, 605, 1687, 3609, 6611, 10933, 16815, 24497, 34219, 46221, 60743, 78025, 98307, 121829, 148831, 179553, 214235, 253117, 296439, 344441, 397363, 455445, 518927, 588049, 663051, 744173, 831655, 925737, 1026659, 1134661, 1249983, 1372865, 1503547 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence starts with a central dot and expands outward with (n-1) centered polygonal pyramids producing a small rhombicosidodecahedron.  Each iteration requires the addition of (n-2) edges and (n-1) vertices to complete the centered polygon of each face. [centered triangles (A005448), centered squares (A001844) and centered pentagons (A005891) ]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

OEIS, (Centered_polygons) pyramidal numbers

Wikipedia, Tetrahedral number

Wikipedia, Triangular number

Wikipedia, Centered polygonal number

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = 40*n^3 - 60*n^2 + 22*n - 1.

G.f.: x*(1+x)*(x^2 + 118*x + 1) / (x-1)^4. - R. J. Mathar, Aug 26 2011

PROG

(Excel) copy and paste the formula   =40 *ROW()^3-60 *ROW()^2+22*ROW()-1 fill down to desired size.

(MAGMA) [40*n^3-60*n^2+22*n-1: n in [1..50]]; // Vincenzo Librandi, Aug 30 2011

CROSSREFS

Sequence in context: A248556 A031689 A181679 * A074303 A077379 A135475

Adjacent sequences:  A193248 A193249 A193250 * A193252 A193253 A193254

KEYWORD

nonn

AUTHOR

Craig Ferguson, Jul 19 2011

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 23 14:11 EDT 2019. Contains 325254 sequences. (Running on oeis4.)