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A193253 Great rhombicosidodecahedron with faces of centered polygons. 1
1, 183, 905, 2527, 5409, 9911, 16393, 25215, 36737, 51319, 69321, 91103, 117025, 147447, 182729, 223231, 269313, 321335, 379657, 444639, 516641, 596023, 683145, 778367, 882049, 994551, 1116233, 1247455, 1388577, 1539959, 1701961, 1874943, 2059265, 2255287 (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 great rhombicosidodecahedron. Each iteration requires the addition of n-2 edges and n-1 vertices to complete the centered polygon of each face.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000.

OEIS Wiki, (Centered_polygons) pyramidal numbers.

Eric W. Weisstein, MathWorld: Great Rhombicosidodecahedron.

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) = 60*n^3 - 90*n^2 + 32*n - 1.

G.f.: x*(1 + 179*x + 179*x^2 + x^3)/(1-x)^4 = x*(1+x)*(1 + 178*x + x^2)/(1-x)^4. - Colin Barker, Feb 12 2012

MATHEMATICA

LinearRecurrence[{4, -6, 4, -1}, {1, 183, 905, 2527}, 50] (* Vincenzo Librandi, Feb 18 2012 *)

a[n_]:=60*n^3 - 90*n^2 + 32*n - 1 ; Array[a, 50] (* or *)

CoefficientList[Series[(1 + x)*(1 + 178*x + x^2)/(1 - x)^4 , {x, 0, 50}], x] (* Stefano Spezia, Sep 02 2018 *)

PROG

(Excel) =60*ROW()^3-90*ROW()^2+32*ROW()-1 fill down  to desired size.

(PARI) a(n)=60*n^3-90*n^2+32*n-1 \\ Charles R Greathouse IV, Feb 12 2012

(MAGMA) [60*n^3-90*n^2+32*n-1: n in [1..40]] // Vincenzo Librandi, Feb 18 2012

CROSSREFS

Cf. A001844 (centered squares), A062786 (centered decagons), and A003215 (centered hexagons).

Sequence in context: A261110 A260172 A252070 * A272126 A171563 A061657

Adjacent sequences:  A193250 A193251 A193252 * A193254 A193255 A193256

KEYWORD

nonn,easy

AUTHOR

Craig Ferguson, Jul 19 2011

STATUS

approved

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Last modified June 18 06:56 EDT 2019. Contains 324203 sequences. (Running on oeis4.)