A233326 a(n) = (7^(n+1) - 4) / 3.

1, 15, 113, 799, 5601, 39215, 274513, 1921599, 13451201, 94158415, 659108913, 4613762399, 32296336801, 226074357615, 1582520503313, 11077643523199, 77543504662401, 542804532636815, 3799631728457713, 26597422099203999, 186181954694428001

Offset: 0

Author

Philippe Deléham, Feb 23 2014

Keywords

• nonn
• easy

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; ...

Examples

			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.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (8,-7).

Programs

Magma

[(7^(n+1)-4)/3: n in [0..30]]; // Vincenzo Librandi, Feb 25 2014

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 *)

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.