

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
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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(n1)  a(n2) + 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)/((x1)*(x^26*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



