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A048875
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Generalized Pellian with second term of 6.
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7
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1, 6, 25, 106, 449, 1902, 8057, 34130, 144577, 612438, 2594329, 10989754, 46553345, 197203134, 835365881, 3538666658, 14990032513, 63498796710, 268985219353, 1139439674122, 4826743915841, 20446415337486, 86612405265785, 366896036400626, 1554196550868289
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| 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
| 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
| a(n)=[ (4+sqrt(5))(2+sqrt(5))^n - (4-sqrt(5))(2-sqrt(5))^n ]/2*sqrt(5).
Binomial transform of A134418: (1, 5, 14, 48, 152,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 23 2007
G.f.: (1+2*x)/(1-4*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
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EXAMPLE
| a(n)=4a(n-1)+a(n-2); a(0)=1, a(1)=6.
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MAPLE
| with(combinat): a:=n->2*fibonacci(n-1, 4)+fibonacci(n, 4): seq(a(n), n=1..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008
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MATHEMATICA
| LinearRecurrence[{4, 1}, {1, 6}, 40] (* From Harvey P. Dale, Nov 30 2011 *)
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CROSSREFS
| Cf. A015448, A001076, A001077, A033887.
Cf. A134418.
Sequence in context: A029871 A188178 A147543 * A094669 A100296 A120758
Adjacent sequences: A048872 A048873 A048874 * A048876 A048877 A048878
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Barry E. Williams
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
More terms from Harvey P. Dale, Nov 30 2011
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