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

0,4

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.

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Sequence in context: A022308 A278137 A349977 * A178749 A121980 A347493

Adjacent sequences: A206265 A206266 A206267 * A206269 A206270 A206271

Keyword

nonn

Author

Jair Taylor, Feb 18 2012

Status

approved