A253512 a(n) = (2^n - 1) * (3^(n+2) - 1) / 2.

0, 13, 120, 847, 5460, 33883, 206640, 1249807, 7528620, 45260803, 271831560, 1631788567, 9793126980, 58765944523, 352617206880, 2115767844127, 12694800840540, 76169386305043, 457018061484600, 2742113599608487, 16452697289229300, 98716230809062363

Offset

0,2

Comments

In Hurwitz 1902 see page 17 table for n=4 where N is the number of n-sheeted Riemann surfaces with w branch points.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

A. Hurwitz, Über die Anzahl der Riemann'schen Flächen mit gegebenen Verzweigungspunkten, Math. Ann. 55 (1902) 53-66.

Index entries for linear recurrences with constant coefficients, signature (12,-47,72,-36).

Formula

a(n) = 12*a(n-1) - 47*a(n-2) + 72*a(n-3) - 36*a(n-4) for n > 4. - Colin Barker, Jan 09 2015

G.f.: x*(18*x^2-36*x+13) / ((x-1)*(2*x-1)*(3*x-1)*(6*x-1)). - Colin Barker, Jan 09 2015

Mathematica

Table[(2^n -1)*(3^(n+2) -1)/2, {n, 0, 30}] (* G. C. Greubel, Aug 03 2018 *)
LinearRecurrence[{12, -47, 72, -36}, {0, 13, 120, 847}, 30] (* Harvey P. Dale, Feb 17 2023 *)

Prog

(PARI) {a(n) = if( n<0, 0, (2^n - 1) * (3^(n+2) - 1) / 2)};
(Magma) [(2^n -1)*(3^(n+2) -1)/2: n in [0..30]]; // G. C. Greubel, Aug 03 2018

Crossrefs

Sequence in context: A016285 A121086 A159969 * A295048 A295376 A188709

Adjacent sequences: A253509 A253510 A253511 * A253513 A253514 A253515

Keyword

nonn,easy

Author

Michael Somos, Jan 02 2015

Status

approved