A238276 a(n) = (9*8^n - 2)/7.

1, 10, 82, 658, 5266, 42130, 337042, 2696338, 21570706, 172565650, 1380525202, 11044201618, 88353612946, 706828903570, 5654631228562, 45237049828498, 361896398627986, 2895171189023890, 23161369512191122, 185290956097528978, 1482327648780231826

Offset: 0

Author

Philippe Deléham, Feb 21 2014

Keywords

• nonn
• easy

Comments

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

Examples

			a(0) = 1;
a(1) = 1 + 8 + 1 = 10;
a(2) = 1 + 8 + 64 + 8 + 1 = 82;
a(3) = 1 + 8 + 64 + 512 + 64 + 8 + 1 = 658; 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. Similar sequences: A151575, A000012, A040000, A005408, A033484, A048473, A020989, A057651, A061801, A238275, this sequence, A138894, A090843, A199023.

Cf. A112468, A112739.

Programs

Magma

[(9*8^n - 2)/7: n in [0..30]]; // Vincenzo Librandi, Feb 23 2014

Mathematica

Table[(9 8^n - 2)/7, {n, 0, 50}] (* Vincenzo Librandi, Feb 23 2014 *)

Formula

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

a(n) = 8*a(n-1) + 2, a(0) = 1.

a(n) = 9*a(n-1) - 8*a(n-2), a(0) = 1, a(1) = 10.

a(n) = Sum_{k=0..n} A112468(n,k)*9^k.

Extensions

Corrected by Vincenzo Librandi, Feb 23 2014