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A049775
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Sum of even-indexed terms of n-th row of array T given by A049773.
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8
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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; internal format)
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OFFSET
| 2,1
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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 (cyrek(AT)cyreksoft.yorks.com), Aug 19 2003
If the offset is set to zero, the inverse Binomial transform gives A007051 without its leading 1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 26 2009]
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FORMULA
| a(n) = 2^(n-3)[3*2^(n-2)+1] - Carl R. White (cyrek(AT)cyreksoft.yorks.com), Aug 19 2003
a(n+1) = 4*a(n) - 2^(n-2); see also A007582 . a(n+1) = 2^(n-2)*A004119(n) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 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 (mathar(AT)strw.leidenuniv.nl), Mar 26 2009]
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CROSSREFS
| A049775(n+2) = A007582(n+1)-A007582(n).
Cf. A029837, A003070.
Sequence in context: A113436 A126223 A114121 * A101850 A176280 A045868
Adjacent sequences: A049772 A049773 A049774 * A049776 A049777 A049778
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| More terms from Michael Somos.
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