A047260 -id:A047260 - cp's OEIS frontend

A113828 a(n) = Sum[2^(A047260(i)-1), {i,1,n}].

1, 9, 25, 57, 121, 633, 1657, 3705, 7801, 40569, 106105, 237177, 499321, 2596473, 6790777, 15179385, 31956601, 166174329, 434609785, 971480697, 2045222521, 10635157113, 27815026297, 62174764665, 130894241401, 680650055289

Offset: 1

Artur Jasinski, Jan 27 2006

			a(2) = 2^(A047260(1)-1) + 2^(A047260(2)-1) = 2^0 + 2^3 = 9

Cf. A047260.

a = {}; s = 0; For[n = 1, n < 41, n++, If[Length[Intersection[{Mod[n, 6]}, {0, 1, 4, 5}]] > 0, s = s + 2^(n - 1); AppendTo[a, s]]]; a

Empirical g.f.: x*(32*x^3+16*x^2+8*x+1) / ((x-1)*(8*x^2-1)*(8*x^2+1)). - Colin Barker, Sep 01 2013

Edited by Stefan Steinerberger, Jul 23 2007

A047243 Numbers that are congruent to {2, 3} mod 6.

Original entry on oeis.org

2, 3, 8, 9, 14, 15, 20, 21, 26, 27, 32, 33, 38, 39, 44, 45, 50, 51, 56, 57, 62, 63, 68, 69, 74, 75, 80, 81, 86, 87, 92, 93, 98, 99, 104, 105, 110, 111, 116, 117, 122, 123, 128, 129, 134, 135, 140, 141, 146, 147, 152, 153, 158, 159, 164, 165, 170, 171, 176, 177, 182, 183

Offset: 1

N. J. A. Sloane

Solutions to 3^x - 2^x == 5 (mod 7). - Cino Hilliard, May 09 2003

Emil Grosswald, Topics From the Theory of Numbers, 1966, p. 65, problem 23.

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A030531. Complement of A047260.

List([1..70], n-> 3*n-2-(-1)^n) # G. C. Greubel, Jun 30 2019

[3*n-2-(-1)^n: n in [1..70]]; // G. C. Greubel, Jun 30 2019

Select[Range[0, 210], MemberQ[{2, 3}, Mod[#, 6]] &] (* or *)
Fold[Append[#1, 6 #2 - Last@ #1 - 7] &, {2}, Range[2, 70]] (* or *)
Rest@ CoefficientList[Series[x(2+x+3x^2)/((1+x)(1-x)^2), {x, 0, 70}], x] (* Michael De Vlieger, Jan 12 2018 *)

vector(70, n, 3*n-2-(-1)^n) \\ G. C. Greubel, Jun 30 2019

[3*n-2-(-1)^n for n in (1..70)] # G. C. Greubel, Jun 30 2019

a(n) = 6*n - 7 - a(n-1), with a(1)=2. - Vincenzo Librandi, Aug 05 2010
G.f.: x*(2+x+3*x^2) / ( (1+x)*(1-x)^2 ). - R. J. Mathar, Oct 08 2011
From Guenther Schrack, Jun 21 2019: (Start)
a(n) = a(n-2) + 6 with a(1)=2, a(2)=3 for n > 2;
a(n) = 3*n - 2 - (-1)^n. (End)
E.g.f.: 3 - 3*(1-x)*cosh(x) - (1-3*x)*sinh(x). - G. C. Greubel, Jun 30 2019
E.g.f.: 3 + (3*x-3)*exp(x) + 2*sinh(x). - David Lovler, Jul 16 2022
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(12*sqrt(3)) + log(3)/4 - log(2)/3. - Amiram Eldar, Dec 13 2021

More terms from Cino Hilliard, May 09 2003

cp's OEIS Frontend

A113828 a(n) = Sum[2^(A047260(i)-1), {i,1,n}].

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A047243 Numbers that are congruent to {2, 3} mod 6.

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