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Search: id:A034478
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| 1, 3, 13, 63, 313, 1563, 7813, 39063, 195313, 976563, 4882813, 24414063, 122070313, 610351563, 3051757813, 15258789063, 76293945313, 381469726563, 1907348632813, 9536743164063, 47683715820313
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Terms are also the quotients arising from sequence A050621.
Binomial transform of A081294. - Paul Barry (pbarry(AT)wit.ie), Jan 13 2005
a(n)^2 + (a(n) - 1)^2 = a(2n). E.g. 63^2 + 62^2 = 7813 = a(6). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 17 2006
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FORMULA
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E.g.f.: exp(3x)cosh(2x). - Paul Barry (pbarry(AT)wit.ie), Mar 17 2003
Partial sums of A020699. G.f.: (1-3x)/((1-x)(1-5x)) - Paul Barry (pbarry(AT)wit.ie), Sep 03 2003
a(n)=sum{k=0..n, sum{j=0..k, C(n, k)C(2k, 2j)}} - Paul Barry (pbarry(AT)wit.ie), Jan 13 2005
a(n) = 6a(n-1) - 5a(n-2), a(0) = 1, a(1) = 3 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 11 2005
a(n)=(5^(n+1) + 1)/2, n>=-1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2007
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MAPLE
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seq((5^(n+1) + 1)/2, n=-1..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2007
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PROGRAM
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sage: [lucas_number2(n, 6, 5)/2 for n in xrange(0, 22)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2008
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CROSSREFS
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Cf. A050621.
Sequence in context: A122122 A093424 A092467 this_sequence A026715 A001850 A130525
Adjacent sequences: A034475 A034476 A034477 this_sequence A034479 A034480 A034481
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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