A233328 a(n) = (2*8^(n+1) - 9) / 7.

1, 17, 145, 1169, 9361, 74897, 599185, 4793489, 38347921, 306783377, 2454267025, 19634136209, 157073089681, 1256584717457, 10052677739665, 80421421917329, 643371375338641, 5146971002709137, 41175768021673105, 329406144173384849, 2635249153387078801

Offset: 0

Author

Philippe Deléham, Feb 23 2014

Keywords

• nonn
• easy

Comments

Sum of n-th row of triangle of powers of 8: 1; 8 1 8; 64 8 1 8 64 ; 512 64 8 1 8 64 512; ...

Examples

			a(0) = 1;
a(1) = 8 + 1 + 8 = 17;
a(2) = 64 + 8 + 1 + 8 + 64 = 145;
a(3) = 512 + 64 + 8 + 1 + 8 + 64 + 512 = 1169; etc.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (9,-8).

Crossrefs

Cf. A226308

Programs

Magma

[(2*8^(n+1)-9)/7: n in [0..30]]; // Vincenzo Librandi, Feb 25 2014

Mathematica

Table[(2 8^(n + 1) - 9)/7, {n, 0, 30}] (* Vincenzo Librandi, Feb 25 2014 *)
LinearRecurrence[{9,-8},{1,17},30] (* Harvey P. Dale, Apr 29 2019 *)

Formula

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

a(n) = 9*a(n-1) - 8*a(n-2) for n>1, a(0)=1, a(1)=17.

a(n) = 8*a(n-1) + 9 for n>0, a(0)=1.

a(n) = A226308(3n+1).