A221875 Numbers m such that 10*m^2 - 6 is a square.

1, 7, 31, 265, 1177, 10063, 44695, 382129, 1697233, 14510839, 64450159, 551029753, 2447408809, 20924619775, 92937084583, 794584521697, 3529161805345, 30173287204711, 134015211518527, 1145790329257321, 5089048875898681, 43509859224573487

Offset

1,2

Comments

See the first two comments on A221874.

For the corresponding numbers whose square is 10*m^2 - 6, see A281647. - Jon E. Schoenfield, Aug 05 2023

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,38,0,-1).

Formula

G.f.: x*(1-x)*(1+8*x+x^2)/((1-6*x-x^2)*(1+6*x-x^2)).

a(n) = ((5-t*(-1)^n)*(3+t)^(2*floor(n/2)) + (5+t*(-1)^n)*(3-t)^(2*floor(n/2)))/10, where t=sqrt(10).

a(n)*a(n-3) - a(n-1)*a(n-2) = 36 + 12(-1)^n.

Mathematica

LinearRecurrence[{0, 38, 0, -1}, {1, 7, 31, 265}, 22]

Prog

(Magma)
m:=22; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x)*(1+8*x+x^2)/((1-6*x-x^2)*(1+6*x-x^2))));
(Maxima)
makelist(expand(((5-sqrt(10)*(-1)^n)*(3+sqrt(10))^(2*floor(n/2))+(5+sqrt(10)*(-1)^n)*(3-sqrt(10))^(2*floor(n/2)))/10), n, 1, 22);
(Magma) I:=[1, 7, 31, 265]; [n le 4 select I[n] else 38*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Mar 25 2013

Crossrefs

Cf. A221874, A281647.

Sequence in context: A241456 A094711 A333735 * A143564 A352411 A344787

Adjacent sequences: A221872 A221873 A221874 * A221876 A221877 A221878

Keyword

nonn,easy

Author

Bruno Berselli, Jan 28 2013

Status

approved