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A049775 Sum of even-indexed terms of n-th row of array T given by A049773. 8
2, 7, 26, 100, 392, 1552, 6176, 24640, 98432, 393472, 1573376, 6292480, 25167872, 100667392, 402661376, 1610629120, 6442483712, 25769869312, 103079346176, 412317122560, 1649267965952, 6597070815232, 26388281163776 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

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. [From R. J. Mathar, Mar 26 2009]

LINKS

Table of n, a(n) for n=2..24.

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

FORMULA

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

a(n+1) = 4*a(n) - 2^(n-2); see also A007582 . a(n+1) = 2^(n-2)*A004119(n) . - Philippe Deléham, Feb 20 2004

a(n)=6*a(n-1)-8*a(n-2). G.f.: -x^2*(-2+5*x)/((4*x-1)*(2*x-1)). [From R. J. Mathar, Mar 26 2009]

MATHEMATICA

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

CROSSREFS

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

Cf. A029837, A003070.

Sequence in context: A126223 A273320 A114121 * A101850 A279002 A176280

Adjacent sequences:  A049772 A049773 A049774 * A049776 A049777 A049778

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Michael Somos.

STATUS

approved

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Last modified June 28 04:43 EDT 2017. Contains 288813 sequences.