A233325 a(n) = (2*6^(n+1) - 7) / 5.

1, 13, 85, 517, 3109, 18661, 111973, 671845, 4031077, 24186469, 145118821, 870712933, 5224277605, 31345665637, 188073993829, 1128443962981, 6770663777893, 40623982667365, 243743896004197, 1462463376025189, 8774780256151141, 52648681536906853

Offset: 0

Author

Philippe Deléham, Feb 23 2014

Keywords

• nonn
• easy

Comments

Sum of n-th row of triangle of powers of 6: 1; 6 1 6; 36 6 1 6 36; 216 36 6 1 6 36 216; ...

Examples

			a(0) = 1;
a(1) = 6 + 1 + 6 = 13;
a(2) = 36 + 6 + 1 + 6 + 36 = 85;
a(3) = 216 + 36 + 6 + 1 + 6 + 36 + 216 = 517; etc.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (7,-6).

Crossrefs

Cf. A026567.

Programs

Magma

[(2*6^(n+1) - 7) / 5: n in [0..30]]; // Vincenzo Librandi, Feb 25 2014

Mathematica

Table[(2 6^(n + 1) - 7)/5, {n, 0, 20}] (* Vincenzo Librandi, Feb 25 2014 *)

Formula

G.f.: (1+6*x)/((1-x)*(1-6*x)).

a(n) = 7*a(n-1) - 6*a(n-2) for n>1, a(0)=1, a(1)=13.

a(n) = 6*a(n-1) + 7 for n>0, a(0)=1.

a(n) = A026567(2*n). - Philippe Deléham, Feb 24 2014