A180226 a(n) = 4*a(n-1) + 10*a(n-2), with a(1)=0 and a(2)=1.

0, 1, 4, 26, 144, 836, 4784, 27496, 157824, 906256, 5203264, 29875616, 171535104, 984896576, 5654937344, 32468715136, 186424233984, 1070384087296, 6145778689024, 35286955629056, 202605609406464, 1163291993916416, 6679224069730304, 38349816218085376

Offset

1,3

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (4, 10).

Formula

a(n) = ((2+sqrt(14))^(n-1) - (2-sqrt(14))^(n-1))/(2*sqrt(14)). - Rolf Pleisch, May 14 2011

G.f.: x^2/(1-4*x-10*x^2).

Mathematica

Join[{a=0, b=1}, Table[c=4*b+10*a; a=b; b=c, {n, 100}]]
LinearRecurrence[{4, 10}, {0, 1}, 30] (* G. C. Greubel, Jan 16 2018 *)

Prog

(PARI) x='x+O('x^30); concat([0], Vec(x^2/(1-4*x-10*x^2))) \\ G. C. Greubel, Jan 16 2018
(Magma) I:=[0, 1]; [n le 2 select I[n] else 4*Self(n-1) + 10*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 16 2018

Crossrefs

Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015443, A015447, A030195, A053404, A057087, A083858, A085939, A090017, A091914, A099012, A180222.

Sequence in context: A197964 A100236 A229278 * A325587 A223627 A144068

Adjacent sequences: A180223 A180224 A180225 * A180227 A180228 A180229

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jan 16 2011

Status

approved