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Search: id:A048876
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| A048876 |
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Generalized Pellian with second term of 7. |
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+0
6
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| 1, 7, 29, 123, 521, 2207, 9349, 39603, 167761, 710647, 3010349, 12752043, 54018521, 228826127, 969323029, 4106118243
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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M. Bicknell, A Primer on the Pell Sequence and related sequences, Fib. Quart. Vol. 13, No. 4, (1975), pp. 345-349.
L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Pellian Representations, Fib. Quart. Vol. 10, No. 5, (1972), pp. 449-488.
A. K. Whitford, Binet's Formula Generalized, Fib. Quart. Vol. 15, No. 1, (1977), pp. 21, 24, 29.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n)=[ (1+sqrt(5))(2+sqrt(5))^n + (1-sqrt(5))(2-sqrt(5))^n ]/2.
a(n) = Lucas(3n+1) - Thomas Baruchel (baruchel(AT)users.sourceforge.net), Nov 26 2003
G.f.: (1+3*x)/(1-4*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
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EXAMPLE
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a(n)=4a(n-1)+ a(n-2); a(0)=1, a(1)=7.
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MAPLE
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with(combinat): a:=n->3*fibonacci(n-1, 4)+fibonacci(n, 4): seq(a(n), n=1..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008
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CROSSREFS
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Cf. A033887, A001076, A001077, A015448.
Sequence in context: A066744 A037576 A055427 this_sequence A126394 A074468 A071918
Adjacent sequences: A048873 A048874 A048875 this_sequence A048877 A048878 A048879
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Barry E. Williams
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