OFFSET
0,3
REFERENCES
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
LINKS
Robert Price, Table of n, a(n) for n = 0..999
Stephen Wolfram, A New Kind of Science.
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
FORMULA
a(n) = Sum_{k=0..n-1} Sum_{i=0..k} C(i,k) - (-1)^k. - Wesley Ivan Hurt, Sep 20 2017
a(n) = n + ((-1)^n*(2*n + 1) - 1)/4 = n - A001057(n). - Peter Luschny, Feb 11 2019
For n > 0: a(n) = (n^2 - 1) mod (2*n + 1). - Ctibor O. Zizka, Mar 11 2025
From Elmo R. Oliveira, Apr 09 2026: (Start)
a(n) = 2*a(n-2) - a(n-4).
G.f.: x^2*(3 + x)/((1 - x)^2*(1 + x)^2). (End)
E.g.f.: (x*cosh(x) + (3*x - 1)*sinh(x))/2. - Stefano Spezia, Apr 11 2026
MAPLE
a := n -> n + ((-1)^n*(2*n + 1) - 1)/4;
seq(a(n), n=0..69); # Peter Luschny, Feb 11 2019
MATHEMATICA
LinearRecurrence[{0, 2, 0, -1}, {0, 0, 3, 1}, 70] (* Jean-François Alcover, Jul 08 2019 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Hans Havermann, May 26 2002
STATUS
approved