A118414 a(n) = (2*n - 1) * (2^n - 1).

1, 9, 35, 105, 279, 693, 1651, 3825, 8687, 19437, 42987, 94185, 204775, 442341, 950243, 2031585, 4325343, 9175005, 19398619, 40894425, 85983191, 180355029, 377487315, 788529105, 1644167119, 3422552013, 7113539531, 14763950025, 30601641927, 63350767557, 130996502467, 270582939585

Offset: 1

Author

Reinhard Zumkeller, Apr 27 2006

Keywords

• nonn
• easy

Comments

Row sums of triangle A118413.

For fixed n, define a triangle T(r,c) counting down the first n odd numbers on the left side, T(r,1) = 2*(n-r)+1, and counting up odd numbers on the right side, T(r,r) = 2*(n+r)-3, r>1. The interior elements are set by T(r,c)=T(r-1,c-1) + T(r-1,c). The sum of all members in this triangle is a(n). - J. M. Bergot, Oct 12 2012

Row sums of triangle A277046. - Miquel Cerda, Sep 28 2016

Examples

			The triangle T(r,c) for n=4 has row(1)=7; row(2) = 5, 9; row(3) = 3, 14, 11; row(4) = 1, 17, 25, 13, and a sum of 7+5+9+...+13 = 105 = a(4). - _J. M. Bergot_, Oct 12 2012
		

Links

• Altug Alkan, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4)

Crossrefs

Cf. A014477, A000225, A005408, A118413, A277046.

Programs

Magma

[(2*n-1)*(2^n-1): n in [1..40]]; // Vincenzo Librandi, Dec 26 2010

Mathematica

Table[(2 n - 1) (2^n - 1), {n, 32}] (* or *)
Rest@ CoefficientList[Series[-x (-1 - 3 x + 6 x^2)/((2 x - 1)^2*(x - 1)^2), {x, 0, 32}], x] (* Michael De Vlieger, Sep 26 2016 *)
LinearRecurrence[{6,-13,12,-4},{1,9,35,105},40] (* Harvey P. Dale, Sep 12 2023 *)

PARI

a(n)=(2*n-1)*(2^n-1) \\ Charles R Greathouse IV, Oct 12 2012

Formula

a(n) = A005408(n-1)*(A000079(n) - 1). Corrected by Omar E. Pol, Sep 26 2016

G.f. -x*(-1-3*x+6*x^2) / ( (2*x-1)^2*(x-1)^2 ). - R. J. Mathar, Oct 15 2012

a(n) = A005408(n-1)*A000225(n). - Miquel Cerda, Sep 26 2016