OFFSET
0,2
COMMENTS
Sum of n-th row of triangle of powers of 7: 1; 7 1 7; 49 7 1 7 49; 343 49 7 1 7 49 343; ...
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (8,-7).
FORMULA
G.f.: (1+7*x)/((1-x)*(1-7*x)).
a(n) = 8*a(n-1) - 7*a(n-2) for n>1, a(0)=1, a(1)=15.
a(n) = 7*a(n-1) + 8 for n>0, a(0)=1.
EXAMPLE
a(0) = 1;
a(1) = 7 + 1 + 7 = 15;
a(2) = 49 + 7 + 1 + 7 + 49 = 113;
a(3) = 343 + 49 + 7 + 1 + 7 + 49 + 343 = 799; etc.
MATHEMATICA
Table[(7^(n + 1) - 4)/3, {n, 0, 40}] (* Vincenzo Librandi, Feb 25 2014 *)
LinearRecurrence[{8, -7}, {1, 15}, 30] (* Harvey P. Dale, Jul 05 2023 *)
PROG
(Magma) [(7^(n+1)-4)/3: n in [0..30]]; // Vincenzo Librandi, Feb 25 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Feb 23 2014
STATUS
approved