A242021 Decimal expansion of the asymptotic growth rate of the number of odd coefficients in Pascal trinomial triangle mod 2.

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

Offset: 0

Author

Jean-François Alcover, Aug 11 2014

Keywords

• nonn
• cons
• easy

Examples

			0.727450913240022814326617235564520452590171035202127753...
		

Links

• Steven Finch, Pascal Sebah and Zai-Qiao Bai, Odd Entries in Pascal's Trinomial Triangle (arXiv:0802.2654) p. 10.

Programs

Mathematica

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

Formula

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