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Search: id:A107839
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| A107839 |
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a(n)=5a(n-1)-2a(n-2); a(0)=1, a(1)=5. |
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+0
2
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| 1, 5, 23, 105, 479, 2185, 9967, 45465, 207391, 946025, 4315343, 19684665, 89792639, 409593865, 1868384047, 8522732505, 38876894431, 177339007145, 808941246863, 3690028220025, 16832258606399, 76781236591945, 350241665746927
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)=A020698(n)-2*A020698(n-1) (n>=1). Kekule numbers for certain benzenoids.
This is the number of spanning, connected subgraphs of the "ladder graph" of n squares (ladder graph = the vertices and edges of the tiling of a 1 x n rectangle by unit squares). - David Pasino (davepasino(AT)yahoo.com), Sep 18 2007
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REFERENCES
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S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 78).
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FORMULA
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a(n)=5a(n-1)=2a(n-2), a(0)=1, a(1)=5.
a(k) = [M^k]_1,2, where M is the 3 by 3 matrix defined as follows: M = [2,1,2;1,1,1;2,1,2]. - Simone Severini (ss54(AT)york.ac.uk), Jun 12 2006
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PROGRAM
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sage: [lucas_number1(n, 5, 2) for n in range(27)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008
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CROSSREFS
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Cf. A020698.
Sequence in context: A129162 A026760 A064914 this_sequence A128732 A026894 A126473
Adjacent sequences: A107836 A107837 A107838 this_sequence A107840 A107841 A107842
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 12 2005
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