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A048876
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a(n) = 4*a(n-1) + a(n-2); a(0)=1, a(1)=7.
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7
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1, 7, 29, 123, 521, 2207, 9349, 39603, 167761, 710647, 3010349, 12752043, 54018521, 228826127, 969323029, 4106118243, 17393796001, 73681302247, 312119004989, 1322157322203, 5600748293801, 23725150497407
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Generalized Pell equation with second term of 7.
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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
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| G.f.: (1+3*x)/(1-4*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
a(n)=[ (1+sqrt(5))*(2+sqrt(5))^n + (1-sqrt(5))*(2-sqrt(5))^n ]/2.
a(n) = Lucas(3*n+1) - Thomas Baruchel (baruchel(AT)users.sourceforge.net), Nov 26 2003
From Gary Detlefs (gdetlefs(AT)aol.com), Mar 06 2011: (Start)
a(n)= Fibonacci(3*n+7) mod Fibonacci(3*n+3), n>0.
a(n)= Fibonacci(3*n+3)-Fibonacci(3*n-1). (End)
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MAPLE
| with(combinat): a:=n->3*fibonacci(n-1, 4)+fibonacci(n, 4): seq(a(n), n=1..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008
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MATHEMATICA
| f[n_] := Block[{s = Sqrt@ 5}, Simplify[((1 + s)(2 + s)^n + (1 - s)(2 - s)^n)/2]]; (* Or *)
f[n_] := Fibonacci[3 n + 3] - Fibonacci[3 n - 1]; (* Or *)
f[n_] := Mod[ Fibonacci[3n + 7], Fibonacci[3n + 3]]; Array[f, 22, 0]
a[n_] := 4a[n - 1] + a[n - 2]; a[0] = 1; a[1] = 7; Array[a, 22, 0] (* Or *)
CoefficientList[ Series[(1 + 3x)/(1 - 4x - x^2), {x, 0, 21}], x] (* RGWv *)
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CROSSREFS
| Cf. A033887, A001076, A001077, A015448.
Sequence in context: A066744 A037576 A055427 * A126394 A074468 A179599
Adjacent sequences: A048873 A048874 A048875 * A048877 A048878 A048879
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams
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