A049775 a(n) is the sum of all integers from 2^(n-2)+1 to 2^(n-1).

2, 7, 26, 100, 392, 1552, 6176, 24640, 98432, 393472, 1573376, 6292480, 25167872, 100667392, 402661376, 1610629120, 6442483712, 25769869312, 103079346176, 412317122560, 1649267965952, 6597070815232, 26388281163776

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Comments

Name when submitted: Sum of even-indexed terms of n-th row of array T given by A049773 (from Clark Kimberling).

Also sum of integers of which the binary order [A029837] is n: a(n) = Sum_[x | ceiling(log_2(x)) = n ]. E.g., a(7) = 6176 = Apply[Plus, Table[w,{w,65,128}]].

This sequence may be obtained by filling a complete binary tree left-to-right, row by row with the integers onwards from 2 and then collecting the sums of the rows; e.g., 2, 3+4, 5+6+7+8, 9+10+11+12+13+14+15+16, etc. a(n) is then equal to the sum of row n-1. - Carl R. White, Aug 19 2003

If the offset is set to zero, the inverse binomial transform gives A007051 without its leading 1. - R. J. Mathar, Mar 26 2009

Examples

			a(2) = 2 = 2.
a(3) = 7 = 3 + 4.
a(4) =26 = 5 + 6 + 7 + 8.
..
		

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-8).

Crossrefs

Cf. A049773 (sequence motivating the original definition).

Cf. A049775(n+2) = A007582(n+1) - A007582(n).

Cf. A029837, A003070.

Programs

Mathematica

LinearRecurrence[{6,-8},{2,7},30] (* Harvey P. Dale, Mar 04 2013 *)

Formula

a(n) = 2^(n-3)*(3*2^(n-2)+1). - Carl R. White, Aug 19 2003

From Philippe Deléham, Feb 20 2004: (Start)

a(n+1) = 4*a(n) - 2^(n-2); see also A007582.

a(n+1) = 2^(n-2)*A004119(n). (End)

From R. J. Mathar, Mar 26 2009: (Start)

a(n) = 6*a(n-1) - 8*a(n-2).

G.f.: -x^2*(-2+5*x)/((4*x-1)*(2*x-1)). (End)

Extensions

More terms from Michael Somos

Name change by Olivier Gérard, Oct 24 2017