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 A206268 Number of compositions of n with at most one 1. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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. = 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

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Last modified August 3 10:11 EDT 2024. Contains 374885 sequences. (Running on oeis4.)