A260160 a(n) = a(n-2) + a(n-6) - a(n-8) with n>8, the first eight terms are 0 except that for a(5) = a(7) = 1.

0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 3, 0, 3, 0, 3, 0, 4, 0, 4, 0, 4, 0, 5, 0, 5, 0, 5, 0, 6, 0, 6, 0, 6, 0, 7, 0, 7, 0, 7, 0, 8, 0, 8, 0, 8, 0, 9, 0, 9, 0, 9, 0, 10, 0, 10, 0, 10, 0, 11, 0, 11, 0, 11, 0, 12, 0, 12, 0, 12, 0, 13, 0, 13, 0, 13, 0, 14, 0, 14, 0, 14

Offset: 1

Author

Jean-François Alcover and Paul Curtz, Nov 09 2015

Keywords

• nonn
• easy

Comments

Sequence related to A264041 (1 is the offset of A264041).

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,0,1,0,-1).

Crossrefs

Cf. A000004 (second bisection), A000217, A002264 (for the first bisection), A264041.

Programs

Maple

with(numtheory): P:= proc(q) local n; for n from 0 to q do
print((1-(-1)^n)*floor(n/6+1/3)/2); od; end: P(100); # Paolo P. Lava, Nov 12 2015

Mathematica

LinearRecurrence[{0, 1, 0, 0, 0, 1, 0, -1}, {0, 0, 0, 0, 1, 0, 1, 0}, 100]
Table[(1 - (-1)^n) (Floor[n/6 + 1/3]/2), {n, 1, 90}] (* Bruno Berselli, Nov 10 2015 *)

PARI

concat(vector(4), Vec(x^5/(1-x^2-x^6+x^8) + O(x^100))) \\ Altug Alkan, Nov 10 2015

Sage

[(1-(-1)^n)*floor(n/6+1/3)/2 for n in (1..90)] # Bruno Berselli, Nov 10 2015

Formula

G.f.: x^5/(1-x^2-x^6+x^8).

a(n) = A264041(n) - n*(n+1)/2, 026).

a(n) = (1-(-1)^n)*floor(n/6+1/3)/2. [Bruno Berselli, Nov 10 2015]