|
%I #8 Aug 13 2014 09:30:39
%S 8,1,9,4,6,9,4,6,2,1,6,5,5,4,0,1,4,6,5,9,5,9,3,7,6,8,4,3,7,7,2,8,5,5,
%T 9,8,6,1,5,1,2,4,6,2,3,5,4,3,1,4,1,2,0,9,3,4,7,1,1,4,6,7,7,5,7,8,5,6,
%U 7,0,3,2,5,0,0,8,1,1,7,9,4,1,6,6,7,6,7,6,7,8,7,9,3,5,8,1,0,9,6,6,7,4,7,4,6
%N Decimal expansion of the asymptotic growth rate of the number of odd coefficients in Pascal "sextinomial" triangle mod 2, where coefficients are from (1+x+x^2+x^3+x^4+x^5)^n.
%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. 12.
%F log(abs(mu))/log(2) - 1, where mu is the root of x^6 - 4*x^5 + x^4 - x^3 + 8*x^2 + 11*x + 8 with maximum modulus.
%e 0.819469462165540146595937684377285598615124623543141209347...
%t mu = Sort[Table[Root[x^6 - 4*x^5 + x^4 - x^3 + 8*x^2 + 11*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, A241002 (1+x+x^4)^n.
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, Aug 13 2014
|
