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Search: id:A085939
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| A085939 |
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Horadam sequence (0,1,6,4). |
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+0 5
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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; listen)
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OFFSET
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0,3
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COMMENT
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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
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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
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a(n) = s*a(n-1) + r*a(n-2); for n > 1, where a(0) = 0, a(1) = 1, s = 4, r = 6
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EXAMPLE
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a(4) = 112 because a(3) = 22, a(2) = 4, s = 4, r = 6 and (4 * 22) + (6 * 4) = 112.
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CROSSREFS
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Cf. A024318, A000032, A000129.
Adjacent sequences: A085936 A085937 A085938 this_sequence A085940 A085941 A085942
Sequence in context: A144047 A077543 A084157 this_sequence A106835 A025569 A098834
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KEYWORD
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easy,nonn
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AUTHOR
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Ross La Haye (rlahaye(AT)new.rr.com), Aug 16 2003
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