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!)
 A202565 Indices of decagonal numbers which are also pentagonal. 2
 1, 56, 5451, 534106, 52336901, 5128482156, 502538914351, 49243685124206, 4825378603257801, 472837859434140256, 46333284845942487251, 4540189077042929610306, 444892196265361159322701, 43594895044928350684014356, 4271854822206713005874084151 (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->oo, a(n)/a(n-1)) = (sqrt(3)+sqrt(2))^4 = 49+20*sqrt(6). LINKS Table of n, a(n) for n=1..15. Index entries for linear recurrences with constant coefficients, signature (99,-99,1). FORMULA G.f.: x*(1-43*x+6*x^2) / ((1-x)*(1-98*x+x^2)). a(n) = 98*a(n-1)-a(n-2)-36. a(n) = 99*a(n-1)-99*a(n-2)+a(n-3). a(n) = 1/48*(5*sqrt(3)*((sqrt(3)+sqrt(2))^(4n-3)+(sqrt(3)-sqrt(2))^(4n-3))+18). a(n) = ceiling(5/48*sqrt(3)*(sqrt(3)+sqrt(2))^(4n-3)). EXAMPLE The second decagonal number that is also pentagonal is A001107(56) = 12376. Hence a(2)=56. MATHEMATICA LinearRecurrence[{99, -99, 1}, {1, 56, 5451}, 15] CROSSREFS Cf. A202563, A202564, A000326, A001107. Sequence in context: A278324 A009600 A278777 * A213693 A180372 A255960 Adjacent sequences: A202562 A202563 A202564 * A202566 A202567 A202568 KEYWORD nonn,easy AUTHOR Ant King, Dec 22 2011 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 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)