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Search: id:A048655
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| A048655 |
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Generalized Pellian with second term equal to 5. |
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+0
19
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| 1, 5, 11, 27, 65, 157, 379, 915, 2209, 5333, 12875, 31083, 75041, 181165, 437371, 1055907, 2549185, 6154277, 14857739, 35869755, 86597249, 209064253, 504725755, 1218515763, 2941757281, 7102030325
(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, Fibonacci Quarterly, Vol. 13, No. 4, 1975, pp. 345-349.
A. F. Horadam, Basic Properties of a Certain Generalized Sequence of Numbers, Fibonacci Quarterly, Vol. 3, No. 3, 1965, pp. 161-176.
A. F. Horadam, Special Properties of the Sequence W(a, b; p, q), Fibonacci Quarterly, Vol. 5, No. 5, 1967, pp. 424-434.
A. F. Horadam, Pell Identities, Fibonacci Quarterly, Vol. 9, No. 3, 1971, pp. 245-252.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..300
Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n)=2*a(n-1)+a(n-2); a(0)=1, a(1)=5.
a(n)=[ (4+sqrt(2))(1+sqrt(2))^n - (4-sqrt(2))(1-sqrt(2))^n ]/2*sqrt(2).
a(n) = P(n) - 3*P(n+1) + 2*P(n+2) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Jan 18 2005
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MAPLE
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with(combinat): a:=n->3*fibonacci(n-1, 2)+fibonacci(n, 2): seq(a(n), n=1..26); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008
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CROSSREFS
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Cf. A001333, A000129, A048654.
Sequence in context: A032379 A042423 A119503 this_sequence A041671 A095053 A019345
Adjacent sequences: A048652 A048653 A048654 this_sequence A048656 A048657 A048658
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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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