OFFSET
0,2
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; ...
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (9,-8).
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).
EXAMPLE
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.
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 *)
PROG
(Magma) [(2*8^(n+1)-9)/7: n in [0..30]]; // Vincenzo Librandi, Feb 25 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Feb 23 2014
STATUS
approved