A165505 a(0)=1, a(1)=7, a(n) = 42*a(n-2) - a(n-1).

1, 7, 35, 259, 1211, 9667, 41195, 364819, 1365371, 13957027, 43388555, 542806579, 1279512731, 21518363587, 32221171115, 871550099539, 481739087291, 36123365093347, -15890323427125, 1533071657347699, -2200465241286949

Offset: 0

Author

Philippe Deléham, Sep 21 2009

Keywords

• easy
• sign

Comments

a(n)/a(n-1) tends to -7.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,42).

Programs

Magma

[(14*6^n-(-7)^n)/13: n in [0..40]]; // G. C. Greubel, Oct 20 2018

Maple

A165505:=n->(14*6^n-(-7)^n)/13: seq(A165505(n), n=0..30); # Wesley Ivan Hurt, Apr 14 2017

Mathematica

LinearRecurrence[{-1, 42}, {1, 7}, 40] (* G. C. Greubel, Oct 20 2018 *)

PARI

vector(40, n, n--; (14*6^n-(-7)^n)/13) \\ G. C. Greubel, Oct 20 2018

Formula

G.f.: (1+8*x)/(1+x-42*x^2).

a(n) = Sum_{k=0..n} A112555(n,k)*6^k.

a(n) = (14*6^n-(-7)^n)/13. - Klaus Brockhaus, Sep 26 2009

E.g.f.: (14*exp(6*x) - exp(-7*x))/13. - G. C. Greubel, Oct 20 2018