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!)
 A082639 Numbers n such that 2*n*(n+2) is a square. 5
 0, 2, 16, 98, 576, 3362, 19600, 114242, 665856, 3880898, 22619536, 131836322, 768398400, 4478554082, 26102926096, 152139002498, 886731088896, 5168247530882, 30122754096400, 175568277047522, 1023286908188736 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Even-indexed terms are squares. Their square roots form sequence A005319. Odd-indexed terms divided by 2 are squares. Their square roots form the sequence A002315. (Index starts at 0.) LINKS Index entries for linear recurrences with constant coefficients, signature (7,-7,1). FORMULA a(n) = A001541(n) - 1. a(n) = (1/2)*(s^n + t^n) - 1, where s = 3 + 2*sqrt(2), t = 3 - 2*sqrt(2). Note: s=1/t. a(n) = 6*a(n-1) - a(n-2) + 4, a(0)=0, a(1)=2. a(n) = 1/kappa(sqrt(2)/A001542(n)); a(n) = 1/kappa(sqrt(8)/A005319(n)) where kappa(x) is the sum of successive remainders by computing the Euclidean algorithm for (1, x). - Thomas Baruchel, Nov 29 2003 G.f.: -2*x^2*(x+1)/((x-1)*(x^2-6*x+1)). - Colin Barker, Nov 22 2012 MATHEMATICA a[0] = 0; a[1] = 2; a[n_] := a[n] = 6a[n - 1] - a[n - 2] + 4; Table[ a[n], {n, 0, 20}] LinearRecurrence[{7, -7, 1}, {0, 2, 16}, 30] (* Harvey P. Dale, Nov 21 2015 *) CROSSREFS Cf. A002315, A005319. Sequence in context: A002699 A335349 A005058 * A207301 A207105 A207387 Adjacent sequences:  A082636 A082637 A082638 * A082640 A082641 A082642 KEYWORD easy,nonn AUTHOR James R. Buddenhagen, May 15 2003 EXTENSIONS More terms from Robert G. Wilson v, May 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 November 26 07:48 EST 2022. Contains 358353 sequences. (Running on oeis4.)