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A016129
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Expansion of 1/((1-2x)(1-6x)).
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) = sum of n-th row in triangle A100851. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 20 2004
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..900
Index to sequences with linear recurrences with constant coefficients, signature (8,-12)
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FORMULA
| 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.
a(n) = (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]
a(n-1)= ((4+sqrt4)^n-(4-sqrt4)^n)/4 in Fibonacci form. [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]
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MATHEMATICA
| Join[{a=1, b=8}, Table[c=8*b-12*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 19 2011*)
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PROG
| (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]
(MAGMA) [(6^(n+1)-2^(n+1))/4 : n in [0..20]]; // Vincenzo Librandi, Oct 09 2011
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CROSSREFS
| Cf. A089278, A089500.
Sequence in context: A080279 A125345 A111996 * A006631 A205218 A126503
Adjacent sequences: A016126 A016127 A016128 * A016130 A016131 A016132
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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