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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A081065 Numbers n such that n^2 = (1/3)*(n+floor(sqrt(3)*n*floor(sqrt(3)*n))). 2
 2, 24, 330, 4592, 63954, 890760, 12406682, 172802784, 2406832290, 33522849272, 466913057514, 6503259955920, 90578726325362, 1261598908599144, 17571805994062650, 244743685008277952, 3408839784121828674, 47479013292697323480, 661297346313640700042 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n)/2 gives indices of pentagonal numbers which are also triangular. a(n) itself gives x-values solving the Diophantine equation 2*x^2 + (x-1)^2 = y^2. LINKS Index entries for linear recurrences with constant coefficients, signature (15,-15,1). FORMULA a(n) = 15*a(n-1) - 15*a(n-2) + a(n-3). a(n) = 14*a(n-1) - a(n-2) - 4. [Sture Sjöstedt, May 02 2011] G.f.: 2*(1-3*x)/((1-x)*(1-14*x+x^2)). - Bruno Berselli, Nov 11 2011 MATHEMATICA LinearRecurrence[{15, -15, 1}, {2, 24, 330}, 20] (* Harvey P. Dale, Mar 14 2016 *) PROG (PARI) Vec(2*(1-3*x)/((1-x)*(1-14*x+x^2)) + O(x^40)) \\ Michel Marcus, Nov 17 2014 CROSSREFS Cf. A046090, A046174, A046175. Sequence in context: A181174 A209290 A333715 * A043699 A220317 A220340 Adjacent sequences: A081062 A081063 A081064 * A081066 A081067 A081068 KEYWORD nonn,easy AUTHOR Benoit Cloitre, Apr 15 2003 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 December 1 07:34 EST 2022. Contains 358454 sequences. (Running on oeis4.)