cp's OEIS Frontend

A242048 Decimal expansion of the asymptotic growth rate of the number of odd coefficients in Pascal "septinomial" triangle mod 2, where coefficients are from (1+x+...+x^5+x^6)^n.

%I A242048 #9 Aug 13 2014 09:30:46
%S A242048 8,3,1,7,9,6,3,9,6,7,3,4,4,4,0,6,8,9,9,9,3,8,9,3,1,0,7,4,5,8,6,6,8,9,
%T A242048 5,7,3,2,5,9,2,8,5,5,8,5,0,2,1,3,7,7,2,2,0,5,5,3,5,0,0,4,2,1,6,0,7,8,
%U A242048 0,6,2,5,8,3,6,6,4,4,6,5,7,6,3,6,4,8,7,7,5,2,3,1,9,6,9,8,8,6,0,3,0,6
%N A242048 Decimal expansion of the asymptotic growth rate of the number of odd coefficients in Pascal "septinomial" triangle mod 2, where coefficients are from (1+x+...+x^5+x^6)^n.
%H A242048 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. 13.
%F A242048 log(abs(mu))/log(2) - 1, where mu is the root of x^6 - x^5 - 2*x^4 - 28*x^3 + 16*x + 64 with maximum modulus.
%e A242048 0.83179639673444068999389310745866895732592855850213772205535...
%t A242048 mu = Sort[Table[Root[x^6 - x^5 - 2*x^4 - 28*x^3 + 16*x + 64, x, n], {n, 1, 5}], N[Abs[#1]] < N[Abs[#2]]&] // Last; RealDigits[Log[mu]/Log[2] - 1, 10, 102] // First
%Y A242048 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, A242047 (1+x+...+x^4+x^5)^n.
%K A242048 nonn,cons
%O A242048 0,1
%A A242048 _Jean-François Alcover_, Aug 13 2014