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A085939
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Horadam sequence (0,1,6,4).
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13
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0, 1, 4, 22, 112, 580, 2992, 15448, 79744, 411664, 2125120, 10970464, 56632576, 292353088, 1509207808, 7790949760, 40219045888, 207621882112, 1071801803776, 5532938507776, 28562564853760
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) / a(n-1) converges to 10^1/2 + 2 as n approaches infinity. 10^1/2 + 2 can also be written as 2^1/2 * (2^1/2 + 5^1/2), ((2 * 2^1/2) * Phi) - 2^1/2 + 2 and 2^1/2 * (2^1/2 + (L(n) / F(n))), where L(n) is the n-th Lucas number and F(n) is the n-th Fibonacci number as n approaches infinity.
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LINKS
| Eric Weisstein, Lucas Number
Eric Weisstein, Lucas Sequence
Eric Weisstein, Horadam Sequence
Eric Weisstein, Fibonacci Number
Eric Weisstein, Pell Number
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FORMULA
| a(n) = s*a(n-1) + r*a(n-2); for n > 1, where a(0) = 0, a(1) = 1, s = 4, r = 6
a(n)=((2+sqrt(10))^n-(2-sqrt(10))^n)/(2*sqrt(10)) [From Rolf Pleisch (r_pleisch(AT)gmx.ch), Jul 06 2009]
G.f.: x/(1-4*x-6*x^2). [Colin Barker, Jan 10 2012]
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EXAMPLE
| a(4) = 112 because a(3) = 22, a(2) = 4, s = 4, r = 6 and (4 * 22) + (6 * 4) = 112.
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=4*b+6*a; a=b; b=c, {n, 100}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 16 2011*)
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PROG
| (Other) sage: [lucas_number1(n, 4, -6) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
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CROSSREFS
| Cf. A024318, A000032, A000129.
Sequence in context: A144047 A077543 A084157 * A192470 A106835 A155596
Adjacent sequences: A085936 A085937 A085938 * A085940 A085941 A085942
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KEYWORD
| easy,nonn
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AUTHOR
| Ross La Haye (rlahaye(AT)new.rr.com), Aug 16 2003
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