A193249 - OEIS

%I #25 Sep 08 2022 08:45:58

%S 1,153,755,2107,4509,8261,13663,21015,30617,42769,57771,75923,97525,

%T 122877,152279,186031,224433,267785,316387,370539,430541,496693,

%U 569295,648647,735049,828801,930203,1039555,1157157,1283309,1418311,1562463,1716065,1879417

%N Snub dodecahedron with faces of centered polygons.

%C 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)]

%H Bruno Berselli, <a href="/A193249/b193249.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

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

%F G.f.: x*(1+x)*(1+148*x+x^2)/(1-x)^4.  - _Bruno Berselli_, Jul 22 2011

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

%t Table[(2 n - 1) (25 n^2 - 25 n + 1), {n, 50}] (* _Wesley Ivan Hurt_, Apr 30 2014 *)

%o (Excel)

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

%o (PARI) for(n=1, 34, print1(50*n^3-75*n^2+27*n-1", "));  \\ _Bruno Berselli_, Jul 21 2011

%o (Magma) [50*n^3-75*n^2+27*n-1: n in [1..34]];  // _Bruno Berselli_, Jul 22 2011

%K nonn,easy

%O 1,2

%A _Craig Ferguson_, Jul 19 2011