A241002 - OEIS

%I #69 Nov 30 2014 15:18:42

%S 7,3,6,2,1,1,5,5,5,7,3,9,3,0,7,9,3,1,6,5,4,9,2,0,9,3,8,9,2,4,5,8,0,9,

%T 8,3,1,8,5,0,0,5,7,7,6,4,8,4,5,9,3,6,7,7,3,9,7,9,4,6,9,1,6,8,5,7,9,4,

%U 3,9,4,2,9,8,1,1,4,3,2,3,5,8,1,2,9,4,4,6,8,2,4,4,2,9,0,1,1,1,9,8,2,2,8,9

%N Decimal expansion of the asymptotic growth rate of the number of odd coefficients in Pascal trinomial triangle mod 2, where coefficients are from (1+x+x^4)^n.

%H Jean-Francois Alcover, <a href="/A241002/b241002.txt">Table of n, a(n) for n = 0..103</a>

%H Steven Finch, Pascal Sebah and Zai-Qiao Bai, <a href="http://arXiv.org/abs/0802.2654">Odd Entries in Pascal's Trinomial Triangle</a> (arXiv:0802.2654) p. 11.

%F log(abs(mu))/log(2) - 1, where mu is the root of x^5 - 3*x^4 - 2*x^2 - 8*x + 8 with maximum modulus.

%e 0.7362115557393079316549209389245809831850057764845936773979469...

%t mu = Sort[Table[Root[x^5 - 3*x^4 - 2*x^2 - 8*x + 8, x, n], {n, 1, 5}], N[Abs[#1]] < N[Abs[#2]] &] // Last; RealDigits[Log[mu]/Log[2] - 1, 10, 104] // First

%Y Cf. A242208 (1+x+x^2)^n, A242021 (1+x+x^3)^n, A242022 (1+x+x^2+x^3+x^4)^n.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Aug 13 2014