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A356619 a(n) = number of k-tuples (u(1), u(2), ..., u(k)) with 1 <= u(1) < u(2) < ... < u(k) <= n such that u(i) - u(i-1) <= 3 for i = 2,...,k. 3
0, 1, 4, 11, 25, 52, 103, 198, 374, 699, 1298, 2401, 4431, 8166, 15037, 27676, 50924, 93685, 172336, 316999, 583077, 1072472, 1972611, 3628226, 6673378, 12274287, 22575966, 41523709, 76374043, 140473802, 258371641, 475219576, 874065112, 1607656425 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
G.f.: x*(1 + x + x^2)/((-1 + x)^2*(1 - x - x^2 - x^3)).
a(n) = 3*a(n-1) - 2*a(n-2) - a(n-4) + a(n-5).
a(n) = A221949(n+2)-1 for n >= 0.
MATHEMATICA
maxDiff = 3;
t = Map[Length[Select[Map[{#, Max[Differences[#]]} &,
Drop[Subsets[Range[#]], # + 1]], #[[2]] <= maxDiff &]] &, Range[16]]
FindGeneratingFunction[%, x]
FindLinearRecurrence[t]
LinearRecurrence[{3, -2, 0, -1, 1}, {0, 1, 4, 11, 25}, 45]
CROSSREFS
Sequence in context: A014162 A014169 A113684 * A014173 A290986 A209232
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Aug 24 2022
STATUS
approved

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Last modified June 24 10:07 EDT 2024. Contains 373674 sequences. (Running on oeis4.)