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A048878
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Generalized Pellian with second term of 9.
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4
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1, 9, 37, 157, 665, 2817, 11933, 50549, 214129, 907065, 3842389, 16276621, 68948873, 292072113, 1237237325, 5241021413, 22201322977, 94046313321, 398386576261, 1687592618365, 7148757049721, 30282620817249
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 0..1584
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (4,1).
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FORMULA
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a(n) = ( (7+sqrt(5))(2+sqrt(5))^n - (7-sqrt(5))(2-sqrt(5))^n )/2*sqrt(5).
G.f.: (1+5*x)/(1-4*x-x^2). [Philippe Deléham, Nov 03 2008]
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EXAMPLE
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a(n) = 4a(n-1) + a(n-2); a(0)=1, a(1)=9.
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MAPLE
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with(combinat): a:=n->5*fibonacci(n-1, 4)+fibonacci(n, 4): seq(a(n), n=1..16); # Zerinvary Lajos, Apr 04 2008
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MATHEMATICA
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LinearRecurrence[{4, 1}, {1, 9}, 31] (* or *) CoefficientList[ Series[ (1+5x)/(1-4x-x^2), {x, 0, 30}], x] (* Harvey P. Dale, Jul 12 2011 *)
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PROG
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(PARI) { default(realprecision, 2000); for (n=0, 2000, a=round(((7+sqrt(5))*(2+sqrt(5))^n - (7-sqrt(5))*(2-sqrt(5))^n )/10*sqrt(5)); if (a > 10^(10^3 - 6), break); write("b048878.txt", n, " ", a); ); } \\ Harry J. Smith, May 31 2009
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CROSSREFS
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Cf. A015448, A001077, A001076, A033887.
Sequence in context: A257448 A288415 A026620 * A246315 A232250 A201441
Adjacent sequences: A048875 A048876 A048877 * A048879 A048880 A048881
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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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STATUS
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approved
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