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

%I A071045 #32 Mar 11 2025 13:24:50
%S A071045 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,
%T A071045 13,42,14,45,15,48,16,51,17,54,18,57,19,60,20,63,21,66,22,69,23,72,24,
%U A071045 75,25,78,26,81,27,84,28,87,29,90,30,93,31,96,32,99,33,102,34
%N A071045 Number of 0's in n-th row of triangle in A071030.
%D A071045 Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
%H A071045 Robert Price, <a href="/A071045/b071045.txt">Table of n, a(n) for n = 0..999</a>
%H A071045 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A071045 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A071045 a(n) = Sum_{k=0..n-1} Sum_{i=0..k} C(i,k) - (-1)^k. - _Wesley Ivan Hurt_, Sep 20 2017
%F A071045 a(n) = n + ((-1)^n*(2*n + 1) - 1)/4 = n - A001057(n). - _Peter Luschny_, Feb 11 2019
%F A071045 For n > 0: a(n) = (n^2 - 1) mod (2*n + 1). - _Ctibor O. Zizka_, Mar 11 2025
%p A071045 a := n -> n + ((-1)^n*(2*n + 1) - 1)/4;
%p A071045 seq(a(n), n=0..69); # _Peter Luschny_, Feb 11 2019
%t A071045 LinearRecurrence[{0, 2, 0, -1}, {0, 0, 3, 1}, 70] (* _Jean-François Alcover_, Jul 08 2019 *)
%Y A071045 Cf. A001057, A064455, A071030.
%K A071045 nonn,easy
%O A071045 0,3
%A A071045 _Hans Havermann_, May 26 2002