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Search: id:A061647
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| A061647 |
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Beginning at the well for the topograph of a positive definite quadratic form with values 1, 1, 1 at a superbase (i.e. 1, 1 and 1 are the vonorms of the superbase), these numbers indicate the labels of the edges of the topograph on a path of greatest ascent. |
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+0
2
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| 1, 3, 9, 23, 61, 159, 417, 1091, 2857, 7479, 19581, 51263, 134209, 351363, 919881, 2408279, 6304957, 16506591, 43214817, 113137859, 296198761, 775458423, 2030176509, 5315071103, 13915036801, 36430039299, 95375081097
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Form the matrix A=[1,1,1;2,1,0;1,0,0]. a(n) is the sum of the second row elements of A^n. - Paul Barry (pbarry(AT)wit.ie), Sep 22 2004
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REFERENCES
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J. H. Conway, The Sensual (Quadratic) Form, MAA.
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FORMULA
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a(1)=1, a(2)=3, a(3)=9, a(n)=2*a(n-1)+2*a(n-2)-a(n-3) for n > 3
a(n)=Fib(n)^2+Fib(n-1)^2+2Fib(n)Fib(n+1)+3Fib(n-1)Fib(n) [offset 0]. - Paul Barry (pbarry(AT)wit.ie), Sep 22 2004
a(n)=fib(n+1)^2-fib(n-2)^2-(-1)^n - Thomas Baruchel (baruchel(AT)users.sourceforge.net), Jul 29 2005
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EXAMPLE
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a(7)=417 since a(7)=2*a(6)+2*a(5)-a(4)=2*159+2*6-23.
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CROSSREFS
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Sequence in context: A027058 A146818 A026599 this_sequence A077996 A029852 A047085
Adjacent sequences: A061644 A061645 A061646 this_sequence A061648 A061649 A061650
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KEYWORD
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nonn
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AUTHOR
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Darrin Frey (freyd(AT)cedarville.edu), Jun 14 2001
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