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Search: id:A055269
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| A055269 |
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a(n)=4a(n-1)-a(n-2)+3; a(0)=1, a(1)=7. |
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+0
1
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| 1, 7, 30, 116, 437, 1635, 6106, 22792, 85065, 317471, 1184822, 4421820, 16502461, 61588027, 229849650, 857810576, 3201392657, 11947760055, 44589647566, 166410830212, 621053673285
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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I. Adler, Three Diophantine equations - Part II, Fib. Quart., 7 (1969), pps. 181-193.
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 122-125, 194-196.
E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart.,7 (1969), pps. 231-242.
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FORMULA
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a(n)={[(17-5*{2-sqrt(3)})(2+sqrt(3))^n+(5*{2+sqrt(3)}-17)(2-sqrt(3))^n]/[4*sqrt(3)]} -3/2.
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EXAMPLE
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G.f.=(1+2x)/(1-x)(1-4x+x^2). Also the first partial sum of A054491.
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CROSSREFS
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Cf. A001834 and A054491.
Adjacent sequences: A055266 A055267 A055268 this_sequence A055270 A055271 A055272
Sequence in context: A038798 A062455 A085277 this_sequence A026631 A037709 A037611
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, May 10 2000
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
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