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

Author

Vladimir Joseph Stephan Orlovsky, Jan 16 2011

Keywords

• nonn
• easy

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..500
• Index entries for linear recurrences with constant coefficients, signature (4, 10).

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.

Programs

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

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 *)

PARI

x='x+O('x^30); concat([0], Vec(x^2/(1-4*x-10*x^2))) \\ G. C. Greubel, Jan 16 2018

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).