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

0,3

References

S. 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).

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

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

Cf. A001057, A064455, A071030.

Sequence in context: A289444 A069115 A065275 * A274317 A105358 A240691

Adjacent sequences: A071042 A071043 A071044 * A071046 A071047 A071048

Keyword

nonn,easy

Author

Hans Havermann, May 26 2002

Status

approved