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

Author

Craig Ferguson, Jul 19 2011

Keywords

• nonn
• easy

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).

Programs

Excel

=50*ROW()^3-75*ROW()^2+27*ROW()-1 fill down to desired size.

Magma

[50*n^3-75*n^2+27*n-1: n in [1..34]];  // 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 *)

PARI

for(n=1, 34, print1(50*n^3-75*n^2+27*n-1", "));  \\ Bruno Berselli, Jul 21 2011

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