The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A046180 Hexagonal pentagonal numbers. 4
 1, 40755, 1533776805, 57722156241751, 2172315626468283465, 81752926228785223683195, 3076689623521787481625080301, 115788137209866023854693048367775, 4357570752679408318225730700647767185, 163992817590548715438241125333485021875651 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS As n increases, this sequence is approximately geometric with common ratio r = lim_{n->infinity} a(n)/a(n-1) = (2+sqrt(3))^8 = 18817 + 10864*sqrt(3). - Ant King, Dec 13 2011 Dickson calls the terms "triangular, pentagonal and hexagonal" (all hexagonal numbers are also triangular). - Jonathan Sondow, May 06 2014 LINKS Colin Barker, Table of n, a(n) for n = 1..219 L. E. Dickson, History of the Theory of Numbers, vol. II, pp. 19-20. Eric Weisstein's World of Mathematics, Hexagonal Pentagonal Number. Index entries for linear recurrences with constant coefficients, signature (37635,-37635,1). FORMULA a(n) = 37634*a(n-1) - a(n-2) + 3136; g.f.: x*(1+3120*x+15*x^2)/((1-x)*(1-37634*x+x^2)). - Warut Roonguthai Jan 08 2001 a(n+1) = 18817*a(n)+1568+1358*(192*a(n)^2+32*a(n)+1)^0.5 - Richard Choulet, Sep 19 2007 From Ant King, Dec 13 2011: (Start) a(n) = 37635*a(n-1) - 37635*a(n-2) + a(n-3). a(n) = (1/48)*((2+sqrt(3))^(8n-5)+(2-sqrt(3))^(8n-5)-4). a(n) = floor((1/48)*(2+sqrt(3))^(8n-5)). a(n) = (1/48)*((tan(5*Pi/12))^(8n-5)+(tan(Pi/12))^(8n-5)-4). a(n) = floor((1/48)*(tan(5*pi/12))^(8n-5)). (End) MATHEMATICA LinearRecurrence[{37635, -37635, 1}, {1, 40755, 1533776805}, 8] (* Ant King, Dec 13 2011 *) PROG (PARI) Vec(x*(1+3120*x+15*x^2)/((1-x)*(1-37634*x+x^2)) + O(x^20)) \\ Colin Barker, Jun 21 2015 CROSSREFS Cf. A046178, A046179. Sequence in context: A334004 A097238 A249879 * A031668 A164648 A232301 Adjacent sequences: A046177 A046178 A046179 * A046181 A046182 A046183 KEYWORD nonn,easy AUTHOR Eric W. Weisstein STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 19 14:45 EDT 2024. Contains 372698 sequences. (Running on oeis4.)