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Search: id:A016129
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| A016129 |
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Expansion of 1/((1-2x)(1-6x)). |
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+0
18
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| 1, 8, 52, 320, 1936, 11648, 69952, 419840, 2519296, 15116288, 90698752, 544194560, 3265171456, 19591036928, 117546237952, 705277460480, 4231664828416, 25389989101568, 152339934871552, 914039609753600
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) = sum of n-th row in triangle A100851. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 20 2004
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FORMULA
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a(n)= A071951(n+2, 2) = 9*(2*3)^(n-1) - (2*1)^(n-1) = (2^(n-1))*(3^(n+1)-1), n>=0. - Wolfdieter Lang, Nov 07 2003
G.f.: 1/((1-2*x)*(1-6*x)). E.g.f.: (-exp(2*x)+3*exp(6*x))/2.
(6^(n+1)-2^(n+1))/4 - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005
a(n)^2=A144843(n+1). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 26 2008]
((4+sqrt4)^n-(4-sqrt4)^n)/4 in Fibonacci form. Offset 1. a(3)=52. [From Al Hakanson (hawkuu(AT)gmail.com), Dec 31 2008]
a(n)=8*a(n-1)-12*a(n-2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 01 2009]
a(n) =[(6^n - 2^n)/4, n>=1. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
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PROGRAM
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(Other) sage: [lucas_number1(n, 8, 12) for n in xrange(1, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
(Other) sage: [(6^n - 2^n)/4 for n in xrange(1, 21)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
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CROSSREFS
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Cf. A089278, A089500.
Sequence in context: A080279 A125345 A111996 this_sequence A006631 A126503 A155590
Adjacent sequences: A016126 A016127 A016128 this_sequence A016130 A016131 A016132
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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