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Search: id:A048878
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| A048878 |
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Generalized Pellian with second term of 9. |
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+0
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
(list; graph; listen)
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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
Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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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). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 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 (zerinvarylajos(AT)yahoo.com), Apr 04 2008
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PROGRAM
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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); ); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2009]
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CROSSREFS
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Cf. A015448, A001077, A001076, A033887.
Sequence in context: A022276 A165394 A026620 this_sequence A026686 A076174 A117085
Adjacent sequences: A048875 A048876 A048877 this_sequence 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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EXTENSIONS
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Added more terms. Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2009
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