A050935 a(n) = a(n-1) - a(n-3) with a(1)=0, a(2)=0, a(3)=1.
0, 0, 1, 1, 1, 0, -1, -2, -2, -1, 1, 3, 4, 3, 0, -4, -7, -7, -3, 4, 11, 14, 10, -1, -15, -25, -24, -9, 16, 40, 49, 33, -7, -56, -89, -82, -26, 63, 145, 171, 108, -37, -208, -316, -279, -71, 245, 524, 595, 350, -174, -769, -1119, -945, -176, 943, 1888, 2064, 1121, -767, -2831, -3952
Offset: 1
References
- R. Palmaccio, "Average Temperatures Modeled with Complex Numbers", Mathematics and Informatics Quarterly, pp. 9-17 of Vol. 3, No. 1, March 1993.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
- José L. Ramírez, Víctor F. Sirvent, A note on the k-Narayana sequence, Annales Mathematicae et Informaticae, 45 (2015) pp. 91-105.
- Index entries for linear recurrences with constant coefficients, signature (1, 0, -1).
Crossrefs
Programs
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Haskell
a050935 n = a050935_list !! (n-1) a050935_list = 0 : 0 : 1 : zipWith (-) (drop 2 a050935_list) a050935_list -- Reinhard Zumkeller, Jan 01 2012
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Maple
A050935 := proc(n) option remember; if n <= 1 then 0 elif n = 2 then 1 else A050935(n-1)-A050935(n-3); fi; end: seq(A050935(n), n=0..61);
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Mathematica
LinearRecurrence[{1,0,-1},{0,0,1},70] (* Harvey P. Dale, Jan 30 2014 *) -
PARI
a(n)=([0,1,0; 0,0,1; -1,0,1]^(n-1)*[0;0;1])[1,1] \\ Charles R Greathouse IV, Feb 06 2017
Formula
From Paul Barry, Oct 20 2004: (Start)
G.f.: x^2/(1-x+x^3).
a(n+2) = Sum_{k=0..floor(n/3)} binomial(n-2*k, k)*(-1)^k. (End)
G.f.: Q(0)*x^2/2, where Q(k) = 1 + 1/(1 - x*(12*k-1 + x^2)/( x*(12*k+5 + x^2 ) - 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 12 2013
Extensions
Offset adjusted by Reinhard Zumkeller, Jan 01 2012
Comments