A241002 Decimal expansion of the asymptotic growth rate of the number of odd coefficients in Pascal trinomial triangle mod 2, where coefficients are from (1+x+x^4)^n.

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

Offset

0,1

Links

Jean-Francois Alcover, Table of n, a(n) for n = 0..103

Steven Finch, Pascal Sebah and Zai-Qiao Bai, Odd Entries in Pascal's Trinomial Triangle (arXiv:0802.2654) p. 11.

Formula

log(abs(mu))/log(2) - 1, where mu is the root of x^5 - 3*x^4 - 2*x^2 - 8*x + 8 with maximum modulus.

Example

0.7362115557393079316549209389245809831850057764845936773979469...

Mathematica

mu = Sort[Table[Root[x^5 - 3*x^4 - 2*x^2 - 8*x + 8, x, n], {n, 1, 5}], N[Abs[#1]] < N[Abs[#2]] &] // Last; RealDigits[Log[mu]/Log[2] - 1, 10, 104] // 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.

Sequence in context: A201682 A021580 A194557 * A198425 A246203 A354627

Adjacent sequences: A240999 A241000 A241001 * A241003 A241004 A241005

Keyword

nonn,cons

Author

Jean-François Alcover, Aug 13 2014

Status

approved