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

1,8

Comments

The Ze3 sums, see A180662, of triangle A108299 equal the terms of this sequence without the two leading zeros. [Johannes W. Meijer, Aug 14 2011]

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).

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

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);

Mathematica

LinearRecurrence[{1, 0, -1}, {0, 0, 1}, 70] (* Harvey P. Dale, Jan 30 2014 *)

Prog

(Haskell)
a050935 n = a050935_list !! (n-1)
a050935_list = 0 : 0 : 1 : zipWith (-) (drop 2 a050935_list) a050935_list
-- Reinhard Zumkeller, Jan 01 2012
(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

Crossrefs

When run backwards this gives a signed version of A000931.

Cf. A099529.

Apart from signs, essentially the same as A078013.

Cf. A203400 (partial sums).

Sequence in context: A228371 A176971 A247917 * A104769 A078013 A086461

Adjacent sequences: A050932 A050933 A050934 * A050936 A050937 A050938

Keyword

easy,nice,sign

Author

Richard J. Palmaccio (palmacr(AT)pinecrest.edu), Dec 31 1999

Extensions

Offset adjusted by Reinhard Zumkeller, Jan 01 2012

Status

approved