A136010 a(0)=20, a(1)=9; for n >= 0, a(n+2) = 7*a(n+1) + 9*a(n).

20, 9, 243, 1782, 14661, 118665, 962604, 7806213, 63306927, 513404406, 4163593185, 33765791949, 273832882308, 2220722303697, 18009552066651, 146053365199830, 1184459524998669, 9605696961789153, 77900014457512092

Offset

0,1

Comments

From an online IQ test (Adaptive IQ).

Links

G. C. Greubel, Table of n, a(n) for n = 0..999 [Offset shifted by Georg Fischer, Jun 18 2021]

Index entries for linear recurrences with constant coefficients, signature (7,9).

Formula

G.f.: (20 - 131*x)/(1-7*x-9*x^2). - M. F. Hasler, Mar 27 2008

a(n) = (10 + 61/sqrt(85))*(7/2 - sqrt(85)/2)^n + (10 - 61/sqrt(85))*(7/2 + sqrt(85)/2)^n. - Alexander R. Povolotsky, simplified by M. F. Hasler, Mar 29 2008

Maple

A136010:=n -> simplify((10+61/sqrt(85))*(7/2-1/2*sqrt(85))^n+(10-61/sqrt(85))*(7/2+1/2*sqrt(85))^n); # M. F. Hasler, Mar 29 2008

Mathematica

LinearRecurrence[{7, 9}, {20, 9}, 50] (* G. C. Greubel, Feb 21 2017 *)

Prog

(PARI) A136010(n) = { local(y=Mod(x, x^2-85)); lift((10+61/y)*(7/2-1/2*y)^n+(10-61/y)*(7/2+1/2*y)^n)} \\ M. F. Hasler, improved by Max Alekseyev, Mar 29 2008
(PARI) my(x='x+O('x^50)); Vec((20 - 131*x)/(1-7*x-9*x^2)) \\ G. C. Greubel, Feb 21 2017

Crossrefs

Sequence in context: A040384 A078080 A216289 * A091534 A033966 A033340

Adjacent sequences: A136007 A136008 A136009 * A136011 A136012 A136013

Keyword

nonn,easy

Author

Jordan Giedd (jordyg365(AT)gmail.com), Mar 20 2008

Extensions

Definition supplied by Don Reble, Mar 27 2008

Offset corrected by Georg Fischer, Jun 18 2021

Status

approved