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A003481
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a(n) = 7*a(n-1) - a(n-2) + 5.
(Formerly M2120)
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4
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2, 20, 143, 986, 6764, 46367, 317810, 2178308, 14930351, 102334154, 701408732, 4807526975, 32951280098, 225851433716, 1548008755919, 10610209857722, 72723460248140, 498454011879263, 3416454622906706, 23416728348467684, 160500643816367087, 1100087778366101930
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..200
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.
John Riordan and N. J. A. Sloane, Correspondence, 1974
S. M. Tanny and M. Zuker, On a unimodal sequence of binomial coefficients, Discrete Math. 9 (1974), 79-89.
Index entries for linear recurrences with constant coefficients, signature (8,-8,1).
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FORMULA
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a(n) = Fibonacci(4(n+1))-1 = A033888(n+1)-1. - Ralf Stephan, Feb 24 2004, index corrected R. J. Mathar, Sep 18 2008
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MAPLE
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A003481:=(-2-4*z+z**2)/(z-1)/(z**2-7*z+1); # [Simon Plouffe in his 1992 dissertation.]
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MATHEMATICA
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t = {2, 20}; Do[AppendTo[t, 7*t[[-1]] - t[[-2]] + 5], {n, 2, 30}] (* T. D. Noe, Oct 07 2013 *)
nxt[{a_, b_}]:={b, 7b-a+5}; NestList[nxt, {2, 20}, 30][[All, 1]] (* Harvey P. Dale, Aug 11 2019 *)
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CROSSREFS
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Cf. A033888.
Sequence in context: A229454 A003490 A081006 * A000183 A198052 A203216
Adjacent sequences: A003478 A003479 A003480 * A003482 A003483 A003484
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Ralf Stephan, Feb 24 2004
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STATUS
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approved
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