The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A046175 Indices of triangular numbers which are also pentagonal. 9
 0, 1, 20, 285, 3976, 55385, 771420, 10744501, 149651600, 2084377905, 29031639076, 404358569165, 5631988329240, 78443478040201, 1092576704233580, 15217630381229925, 211954248632985376, 2952141850480565345, 41118031658094929460, 572700301362848447101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Colin Barker, Table of n, a(n) for n = 0..874 W. Sierpiński, Sur les nombres pentagonaux, Bull. Soc. Roy. Sci. Liege 33 (1964) 513-517 Eric Weisstein's World of Mathematics, Pentagonal Triangular Number, MathWorld Index entries for linear recurrences with constant coefficients, signature (15,-15,1). FORMULA From Warut Roonguthai, Jan 05 2001: (Start) a(n) = 14*a(n-1) - a(n-2) + 6. G.f.: x*(1+5*x)/((1-x)*(1-14*x+x^2)). (End) a(n+1) = 7*a(n) + 3 + 2*sqrt(12*a(n)^2 + 12*a(n) + 1). - Richard Choulet, Sep 19 2007 a(n+1) = 15*a(n)-15*a(n-1)+ a(n-2) with a(1)=1, a(2)=20, a(3)=285. - Sture Sjöstedt, May 29 2009 a(n) = (1/12)*(-6 + (7 - 4*sqrt(3))^n*(3 + sqrt(3)) - (-3 + sqrt(3))*(7 + 4*sqrt(3))^n). - Alan Michael Gómez Calderón, Jun 30 2024 MATHEMATICA LinearRecurrence[{15, -15, 1}, {0, 1, 20}, 20] (* Harvey P. Dale, Sep 10 2021 *) PROG (PARI) concat(0, Vec(-x*(5*x+1)/((x-1)*(x^2-14*x+1)) + O(x^50))) \\ Colin Barker, Jun 23 2015 CROSSREFS Cf. A014979, A046174, A001834. Sequence in context: A017953 A016317 A021404 * A231105 A016314 A021164 Adjacent sequences: A046172 A046173 A046174 * A046176 A046177 A046178 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 August 11 15:18 EDT 2024. Contains 375073 sequences. (Running on oeis4.)