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| A295955
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Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n) + 1, where a(0) = 3, a(1) = 4, b(0) = 1, b(1) = 2, b(2) = 5, and (a(n)) and (b(n)) are increasing complementary sequences.
(history;
published version)
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#13 by Alois P. Heinz at Sun Sep 27 18:31:50 EDT 2020
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#12 by Georg Fischer at Sun Sep 27 17:26:03 EDT 2020
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#11 by Georg Fischer at Sun Sep 27 17:25:16 EDT 2020
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Discussion
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| Sun Sep 27
| 17:26
| Georg Fischer: Example and MMA had b(1)=2.
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#10 by Georg Fischer at Sun Sep 27 17:24:46 EDT 2020
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| NAME
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Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n) + 1, where a(0) = 3, a(1) = 4, b(0) = 1, b(1) = 12, b(2) = 5, and (a(n)) and (b(n)) are increasing complementary sequences.
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approved
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#9 by N. J. A. Sloane at Thu Feb 22 22:41:12 EST 2018
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#8 by N. J. A. Sloane at Thu Feb 22 22:41:09 EST 2018
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| LINKS
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Clark Kimberling, <a href="/A295955/b295955.txt">Table of n, a(n) for n = 0..99772000</a>
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approved
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#7 by Susanna Cuyler at Fri Dec 08 16:56:00 EST 2017
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#6 by Jon E. Schoenfield at Fri Dec 08 14:55:36 EST 2017
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#5 by Jon E. Schoenfield at Fri Dec 08 14:55:29 EST 2017
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| COMMENTS
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The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values. . a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622).
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proposed
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Discussion
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| Fri Dec 08
| 14:55
| Jon E. Schoenfield: removed 2nd space between sentences
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#4 by Clark Kimberling at Fri Dec 08 10:57:28 EST 2017
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