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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, 238418579101563
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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(2*n). E.g., 63^2 + 62^2 = 7813 = a(6). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 17 2006
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 0..250
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FORMULA
| E.g.f.: exp(3*x)*cosh(2*x). - Paul Barry (pbarry(AT)wit.ie), Mar 17 2003
Partial sums of A020699. G.f.: (1-3*x)/((1-x)*(1-5*x)). - Paul Barry (pbarry(AT)wit.ie), Sep 03 2003
a(n)=sum{k=0..n, sum{j=0..k, C(n, k)*C(2*k, 2*j)}} - Paul Barry (pbarry(AT)wit.ie), Jan 13 2005
a(n) = 6*a(n-1) - 5*a(n-2), a(0) = 1, a(1) = 3. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 11 2005
a(n)=5*a(n-1)-2 with a(0)=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 01 2010]
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EXAMPLE
| For n=1, a(1)=5*1-2=3; n=2, a(2)=5*3-2=13; n=3, a(3)=5*13-2=63 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 01 2010]
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MAPLE
| seq((5^n + 1)/2, n=0..20); # Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2007
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PROG
| 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
| Cf. A050621.
Sequence in context: A093424 A186242 A092467 * A026715 A001850 A130525
Adjacent sequences: A034475 A034476 A034477 * A034479 A034480 A034481
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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