A370188 a(n) = sqrt((A114052(n)^2 - 1)/27)/5.

0, 1, 52, 2703, 140504, 7303505, 379641756, 19734067807, 1025791884208, 53321443911009, 2771689291488260, 144074521713478511, 7489103439809394312, 389289304348375025713, 20235554722675691942764, 1051859556274787605998015, 54676461371566279819954016, 2842124131765171763031610817

Offset

0,3

Comments

5*a(n) are the y-values in solutions to x^2 - 27*y^2 = 1.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..583

Lisa Carbone and Pranav Shankar, Kac-Moody Fibonacci sequences, arXiv:2601.00958 [math.NT], 2026. See p. 14, Table 8.

Index entries for linear recurrences with constant coefficients, signature (52,-1).

Formula

G.f.: x/(1 - 52*x + x^2).

Example

a(2) = 52: A114052(2) = 1351; 1351^2 - 27*(5*52)^2 = 1825201 - 1825200 = 1.

Mathematica

LinearRecurrence[{52, -1}, {0, 1}, 18]

Crossrefs

Cf. A114052.

Sequence in context: A004296 A097837 A247628 * A262272 A189908 A189902

Adjacent sequences: A370185 A370186 A370187 * A370189 A370190 A370191

Keyword

nonn,easy

Author

Hugo Pfoertner, Feb 11 2024

Status

approved