A193249 Snub dodecahedron with faces of centered polygons.

1, 153, 755, 2107, 4509, 8261, 13663, 21015, 30617, 42769, 57771, 75923, 97525, 122877, 152279, 186031, 224433, 267785, 316387, 370539, 430541, 496693, 569295, 648647, 735049, 828801, 930203, 1039555, 1157157, 1283309, 1418311, 1562463, 1716065, 1879417

Offset

1,2

Comments

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

Links

Bruno Berselli, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 50*n^3-75*n^2+27*n-1 = (2*n-1)*(25*n^2-25*n+1).

G.f.: x*(1+x)*(1+148*x+x^2)/(1-x)^4. - Bruno Berselli, Jul 22 2011

Maple

A193249:=n->(2*n-1)*(25*n^2-25*n+1); seq(A193249(n), n=1..50); # Wesley Ivan Hurt, Apr 30 2014

Mathematica

Table[(2 n - 1) (25 n^2 - 25 n + 1), {n, 50}] (* Wesley Ivan Hurt, Apr 30 2014 *)

Prog

(Excel)
=50*ROW()^3-75*ROW()^2+27*ROW()-1 fill down to desired size.
(PARI) for(n=1, 34, print1(50*n^3-75*n^2+27*n-1", "));  \\ Bruno Berselli, Jul 21 2011
(Magma) [50*n^3-75*n^2+27*n-1: n in [1..34]];  // Bruno Berselli, Jul 22 2011

Crossrefs

Sequence in context: A256740 A199851 A181775 * A050209 A109142 A014576

Adjacent sequences: A193246 A193247 A193248 * A193250 A193251 A193252

Keyword

nonn,easy

Author

Craig Ferguson, Jul 19 2011

Status

approved