A187709 a(n) = (7*9^n + 1)/8.

1, 8, 71, 638, 5741, 51668, 465011, 4185098, 37665881, 338992928, 3050936351, 27458427158, 247125844421, 2224132599788, 20017193398091, 180154740582818, 1621392665245361, 14592533987208248, 131332805884874231, 1181995252963868078, 10637957276674812701, 95741615490073314308, 861674539410659828771

Offset: 0

Author

Sture Sjöstedt, Mar 30 2011

Keywords

• nonn
• easy

Comments

Case r=9 in a(n)=((r-2)*r^n+1)/(r-1).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-9).

Crossrefs

Cf. A007051, A083068, A270472 (first differences), A059482: cases r=3,8,10 in ((r-2)*r^n+1)/(r-1), respectively.

Programs

Magma

[(7*9^n+1)/8: n in [0..25]]; // Vincenzo Librandi, Mar 30 2011

Mathematica

(7*9^Range[0,30]+1)/8 (* or *) LinearRecurrence[{10,-9},{1,8},30] (* Harvey P. Dale, Jul 20 2012 *)

PARI

a(n)=(7*9^n+1)/8 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = (7*9^n + 1)/8.

a(n) = +10*a(n-1) -9*a(n-2).

a(n) = 8*Sum_{i=0..n-1} a(i) -n + 1.

G.f.: (1-2*x)/((1-x)*(1-9*x)).

a(n) = 9^n - Sum_{i=0..n-1} 9^i for n>0. - Bruno Berselli, Jun 20 2013

E.g.f.: (7*exp(9*x) + exp(x))/8. - G. C. Greubel, Nov 06 2018

Extensions

Additional formulas from Bruno Berselli