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.

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, 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, 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

Offset

0,1

Links

Table of n, a(n) for n=0..101.

Steven Finch, Pascal Sebah and Zai-Qiao Bai, Odd Entries in Pascal's Trinomial Triangle (arXiv:0802.2654) p. 13.

Formula

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.

Example

0.83179639673444068999389310745866895732592855850213772205535...

Mathematica

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

Crossrefs

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.

Sequence in context: A001061 A259073 A075525 * A097890 A088453 A019782

Adjacent sequences: A242045 A242046 A242047 * A242049 A242050 A242051

Keyword

nonn,cons

Author

Jean-François Alcover, Aug 13 2014

Status

approved