login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

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 the sequence A005319. Odd indexed terms divided by 2 are squares. Their square roots form the sequence A002315. (Index starts at 0.)

LINKS

Table of n, a(n) for n=1..21.

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: A038749 A002699 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 14:38 EST 2019. Contains 329865 sequences. (Running on oeis4.)