A206268 Number of compositions of n with at most one 1.

1, 1, 1, 3, 4, 8, 13, 23, 39, 67, 114, 194, 329, 557, 941, 1587, 2672, 4492, 7541, 12643, 21171, 35411, 59166, 98758, 164689, 274393, 456793, 759843, 1263004, 2097872, 3482269, 5776559, 9576639, 15867427, 26276106, 43489802, 71944217, 118958597, 196605701

Offset: 0

Author

Jair Taylor, Feb 18 2012

Keywords

• nonn

Examples

			We have a(3) = 3 since 3 = 1 + 2 = 2+1.  A(2) = 1 since 2 is the only composition of 2 that does not have more than one 1.
		

Links

• Jair Taylor, Table of n, a(n) for n = 0..499
• Ricardo Gómez Aíza, Symbolic dynamical scales: modes, orbitals, and transversals, arXiv:2009.02669 [math.DS], 2020.

Programs

Mathematica

CoefficientList[Series[(2 x^3 - 2 x^2 - x + 1)/(x^4 + 2 x^3 - x^2 - 2 x + 1), {x, 0, 38}], x] (* Michael De Vlieger, Dec 09 2020 *)

Sage

R. = PowerSeriesRing(QQ)
f = (2*x^3 - 2*x^2 - x + 1)/(x^4 + 2*x^3 - x^2 - 2*x + 1)
print(f.list())

Formula

G.f.: (2*x^3 - 2*x^2 - x + 1)/(x^4 + 2*x^3 - x^2 - 2*x + 1).