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A048879
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Generalized Pellian with second term of 10.
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2
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1, 10, 41, 174, 737, 3122, 13225, 56022, 237313, 1005274, 4258409, 18038910, 76414049, 323695106, 1371194473, 5808472998, 24605086465, 104228818858, 441520361897, 1870310266446, 7922761427681, 33561355977170, 142168185336361, 602234097322614
(list;
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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Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
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) = ((8+sqrt(5))*(2+sqrt(5))^n - (8-sqrt(5))*(2-sqrt(5))^n)2*sqrt(5).
From Philippe Deléham, Nov 03 2008: (Start)
a(n) = 4*a(n-1) + a(n-2); a(0)=1, a(1)=10.
G.f.: (1+6*x)/(1-4*x-x^2). (End)
For n >= 1, a(n) equals the denominator of the continued fraction [4, 4, ..., 4, 10] (with n copies of 4). The numerator of that continued fraction is a(n+1). - ZhenShu Luan, Aug 05 2019
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MAPLE
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with(combinat): a:=n->6*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, 10}, 30] (* Harvey P. Dale, Jul 18 2011 *)
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PROG
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(Haskell)
a048879 n = a048879_list !! n
a048879_list = 1 : 10 : zipWith (+)
a048879_list (map (* 4) $ tail a048879_list)
-- Reinhard Zumkeller, Mar 03 2014
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CROSSREFS
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Cf. A015448, A001077, A001076, A033887.
Sequence in context: A294604 A061003 A211064 * A221805 A089211 A220927
Adjacent sequences: A048876 A048877 A048878 * A048880 A048881 A048882
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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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More terms from Harvey P. Dale, Jul 18 2011
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STATUS
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approved
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