A190960 a(n) = 3*a(n-1) - 6*a(n-2), with a(0)=0, a(1)=1.

0, 1, 3, 3, -9, -45, -81, 27, 567, 1539, 1215, -5589, -24057, -38637, 28431, 317115, 780759, 439587, -3365793, -12734901, -18009945, 22379571, 175198383, 391317723, 122762871, -1979617725, -6675430401, -8148584853, 15606827847, 95711992659, 193495010895

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Taras Goy and Mark Shattuck, Determinants of Toeplitz-Hessenberg Matrices with Generalized Leonardo Number Entries, Ann. Math. Silesianae (2023). See p. 16.

Index entries for linear recurrences with constant coefficients, signature (3,-6).

Formula

G.f.: x/(1-3*x+6*x^2). - Philippe Deléham, Oct 11 2011

Mathematica

LinearRecurrence[{3, -6}, {0, 1}, 50]

Prog

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-3*x+6*x^2))) \\ G. C. Greubel, Jan 25 2018
(Magma) I:=[0, 1]; [n le 2 select I[n] else 3*Self(n-1) - 6*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 25 2018

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Sequence in context: A245023 A038080 A257621 * A257623 A257625 A216147

Adjacent sequences: A190957 A190958 A190959 * A190961 A190962 A190963

Keyword

sign

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Status

approved