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%I #29 Sep 04 2020 13:11:53
%S 3,33,315,2889,26163,235953,2125035,19129689,172180323,1549662273,
%T 13947078555,125524061289,1129717614483,10167461718993,91507165036875,
%U 823564514029689,7412080712360643,66708726669526113,600378540800575995,5403406869529706889
%N a(n) = Sum_{i=3^n..3^(n+1)-1} i.
%C Partial sums give 3, 36, 351, 3240, 29403,...: A026121.
%C 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
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-27).
%F G.f.: 3*(1-x)/(1-12*x+27*x^2). [_Bruno Berselli_, Jun 11 2013]
%F a(n) = 3^(n-1)*(4*3^(n+1)-3). [_Bruno Berselli_, Jun 11 2013]
%F a(0)=3, a(1)=33, a(n)=12*a(n-1)-27*a(n-2). - _Harvey P. Dale_, Jun 19 2013
%e a(0) = 1+2 = 3,
%e a(1) = 3+4+5+6+7+8 = 33.
%t Table[3^(n - 1) (4 3^(n + 1) - 3), {n, 0, 20}] (* _Bruno Berselli_, Jun 11 2013 *)
%t LinearRecurrence[{12,-27},{3,33},30] (* _Harvey P. Dale_, Jun 19 2013 *)
%o (PARI) a(n) = sum(i=3^n, 3^(n+1)-1, i) \\ _Michel Marcus_, Jun 11 2013
%Y Cf. A010035, A010036 (base 2), A026121, A101291 (base 10).
%Y Cf. A007089 (numbers in base 3).
%K nonn,easy
%O 0,1
%A _Michel Marcus_, Jun 10 2013