A226508 a(n) = Sum_{i=3^n..3^(n+1)-1} i.

3, 33, 315, 2889, 26163, 235953, 2125035, 19129689, 172180323, 1549662273, 13947078555, 125524061289, 1129717614483, 10167461718993, 91507165036875, 823564514029689, 7412080712360643, 66708726669526113, 600378540800575995, 5403406869529706889

Offset: 0

Author

Michel Marcus, Jun 10 2013

Keywords

• nonn
• easy

Comments

Partial sums give 3, 36, 351, 3240, 29403,...: A026121.

a(n) is the sum of all integers having n+1 digits in their ternary expansion (without leading zeros). - Jonathan Vos Post, Sep 07 2006

Examples

			a(0) = 1+2 = 3,
a(1) = 3+4+5+6+7+8 = 33.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (12,-27).

Crossrefs

Cf. A010035, A010036 (base 2), A026121, A101291 (base 10).

Cf. A007089 (numbers in base 3).

Programs

Mathematica

Table[3^(n - 1) (4 3^(n + 1) - 3), {n, 0, 20}] (* Bruno Berselli, Jun 11 2013 *)
LinearRecurrence[{12,-27},{3,33},30] (* Harvey P. Dale, Jun 19 2013 *)

PARI

a(n) = sum(i=3^n, 3^(n+1)-1, i) \\ Michel Marcus, Jun 11 2013

Formula

G.f.: 3*(1-x)/(1-12*x+27*x^2). [Bruno Berselli, Jun 11 2013]

a(n) = 3^(n-1)*(4*3^(n+1)-3). [Bruno Berselli, Jun 11 2013]

a(0)=3, a(1)=33, a(n)=12*a(n-1)-27*a(n-2). - Harvey P. Dale, Jun 19 2013