A193251 Small rhombicosidodecahedron with faces of centered polygons.

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

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
(PARI) a(n)=40*n^3-60*n^2+22*n-1 \\ Charles R Greathouse IV, Oct 19 2022

Crossrefs

Sequence in context: A248556 A031689 A181679 * A074303 A077379 A135475

Adjacent sequences: A193248 A193249 A193250 * A193252 A193253 A193254

Keyword

nonn,easy

Author

Craig Ferguson, Jul 19 2011

Status

approved