A052454 Positive integer values of k such that 10*k^2 - 9 is a square.

1, 3, 13, 25, 111, 493, 949, 4215, 18721, 36037, 160059, 710905, 1368457, 6078027, 26995669, 51965329, 230804967, 1025124517, 1973314045, 8764510719, 38927735977, 74933968381, 332820602355, 1478228842609, 2845517484433, 12638418378771

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 38*a(n-3)-a(n-6).

G.f.: x*(1-x)*(1+4*x+17*x^2+4*x^3+x^4)/(1-38*x^3+x^6). [Colin Barker, Jun 13 2012]

Example

25 is a term of the sequence since 10*25^2-9 = 6241 = 79^2.

Mathematica

LinearRecurrence[{0, 0, 38, 0, 0, -1}, {1, 3, 13, 25, 111, 493}, 50] (* Paolo Xausa, Mar 18 2024 *)

Crossrefs

Cf. A077442, A082651, A221874.

Sequence in context: A056714 A120074 A056706 * A330718 A284108 A366939

Adjacent sequences: A052451 A052452 A052453 * A052455 A052456 A052457

Keyword

nonn,easy

Author

John W. Layman, May 20 2003

Extensions

More terms from Bruno Berselli, Jan 29 2013

Status

approved