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Decimal expansion of the asymptotic growth rate of the number of odd coefficients in Pascal quintinomial triangle mod 2.
4

%I #10 Jun 11 2024 08:26:23

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

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

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

%N Decimal expansion of the asymptotic growth rate of the number of odd coefficients in Pascal quintinomial triangle mod 2.

%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. 10.

%F log(abs(mu))/log(2) - 1, where mu = 3.4572905... is the root of x^4 - x^3 - 6*x^2 - 4*x - 16 with maximum modulus.

%e 0.7896418505307685639015472670664140189908295535926838935...

%t mu = Sort[Table[Root[x^4 - x^3 - 6*x^2 - 4*x - 16, x, n], {n, 1, 4}], N[Abs[#1]] < N[Abs[#2]] &] // Last; RealDigits[Log[mu]/Log[2] - 1, 10, 100] // First

%Y Cf. A242021.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Aug 11 2014