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A048655
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Generalized Pellian with second term equal to 5.
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21
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Equals binomial transform of A143095: (1, 4, 2, 8, 4, 16, 8, 32,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 23 2008
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REFERENCES
| 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
| T. D. Noe, Table of n, a(n) for n=0..300
Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
| 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
G.f.: (1+3*x)/(1-2*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
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MAPLE
| 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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MATHEMATICA
| a[n_]:=(MatrixPower[{{1, 2}, {1, 1}}, n].{{4}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 20 2010]
LinearRecurrence[{2, 1}, {1, 5}, 30] (* From Harvey P. Dale, Nov 05 2011 *)
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CROSSREFS
| Cf. A001333, A000129, A048654.
Cf. A143095.
Sequence in context: A042423 A192300 A119503 * A041671 A203160 A095053
Adjacent sequences: A048652 A048653 A048654 * A048656 A048657 A048658
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Barry E. Williams
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