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Search: id:A051959
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| A051959 |
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Linear second order recurrence. |
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+0
1
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| 1, 10, 36, 104, 273, 686, 1688, 4112, 9969, 24114, 58268, 140728, 339809, 820438, 1980784, 4782112, 11545121, 27872474, 67290196, 162453000, 392196337, 946845822, 2285888136
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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A. F. Horadam, Special Properties of the Sequence W(n)(a,b; p,q), Fibonacci Quarterly, Vol. 5,No.5,1967, pp. 424-434.
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FORMULA
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a(n)={[((25/2)+17*sqrt(2)/2)(1+sqrt(2))^n - ((25/2)-17*sqrt(2)/2)(1-sqrt(2))^n]/2*sqrt(2)} - (7n+15)/2
(1/2) [4*Pell(n+2) - 3*Pell(n) - 7n - 15 ], with Pell(n) = A000129(n). - Ralf Stephan, May 15 2007
G.f.: -(1+6*x)/(-1+x)^2/(-1+2*x+x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 16 2007
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EXAMPLE
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a(n)=2a(n-1)+a(n-2)+(7n+1); a(0)=1, a(1)=10.
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CROSSREFS
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Cf. A048771 and A048695.
Sequence in context: A118629 A050509 A118415 this_sequence A117327 A117404 A089222
Adjacent sequences: A051956 A051957 A051958 this_sequence A051960 A051961 A051962
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, Jan 04 2000
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