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Search: id:A102446
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| A102446 |
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a(n) = a(n-1) + 4*a(n-2), a(0) = a(1) = 2. |
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+0
2
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| 2, 2, 10, 18, 58, 130, 362, 882, 2330, 5858, 15178, 38610, 99322, 253762, 651050, 1666098, 4270298, 10934690, 28015882, 71754642, 183818170, 470836738, 1206109418, 3089456370, 7913894042, 20271719522, 51927295690, 133014173778
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OFFSET
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0,1
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COMMENT
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The continued fraction expansion c_0 = 0, c_n = 1/2 (n>0) (see a paper by Bremner & Tzanakis) has convergents 2/1, 2/5, 10/9, 18/29, 58/65, 130/181, ... where the numerators and denominators satisfy the recurrence a_n = a_{n-1} + 4a_{n-2}. The denominators are A006131 and the numerators are the present sequence.
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MATHEMATICA
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a[0] = a[1] = 2; a[n_] := a[n] = a[n - 1] + 4a[n - 2]; Table[ a[n], {n, 0, 27}] (from Robert G. Wilson v Feb 23 2005)
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PROGRAM
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sage: from sage.combinat.sloane_functions import recur_gen2b sage: it = recur_gen2b(2, 2, 1, 4, lambda n: 0) sage: [it.next() for i in range(29)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 09 2008
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CROSSREFS
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Equals 2*A006131(n).
Sequence in context: A015623 A164124 A003609 this_sequence A151456 A151389 A151428
Adjacent sequences: A102443 A102444 A102445 this_sequence A102447 A102448 A102449
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), based on a suggestion from R. K. Guy, Feb 23 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 23 2005
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