A071045 Number of 0's in n-th row of triangle in A071030.

0, 0, 3, 1, 6, 2, 9, 3, 12, 4, 15, 5, 18, 6, 21, 7, 24, 8, 27, 9, 30, 10, 33, 11, 36, 12, 39, 13, 42, 14, 45, 15, 48, 16, 51, 17, 54, 18, 57, 19, 60, 20, 63, 21, 66, 22, 69, 23, 72, 24, 75, 25, 78, 26, 81, 27, 84, 28, 87, 29, 90, 30, 93, 31, 96, 32, 99, 33, 102, 34

Offset: 0

Author

Hans Havermann, May 26 2002

Keywords

• nonn
• easy

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
• Index entries for sequences related to cellular automata
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

Cf. A001057, A064455, A071030.

Programs

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 *)

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