A356621 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) <= 5 for i = 2,...,k.

0, 1, 4, 11, 26, 57, 119, 242, 485, 964, 1907, 3762, 7410, 14583, 28686, 56413, 110924, 218091, 428777, 842976, 1657271, 3258134, 6405349, 12592612, 24756452, 48669933, 95682600, 188107071, 369808798, 727024989, 1429293531, 2809917134, 5524151673

Offset

0,3

Links

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (3,-2,0,0,0,-1,1).

Formula

G.f.: (x (-1 - x - x^2 - x^3 - x^4))/((-1 + x)^2 (-1 + x + x^2 + x^3 + x^4 + x^5)).

a(n) = 3*a(n-1) - 2*a(n-2) - a(n-6) + a(n-7).

Mathematica

maxDiff = 5; t = Map[Length[Select[Map[{#, Max[Differences[#]]} &,
      Drop[Subsets[Range[#]], # + 1]], #[[2]] <= maxDiff &]] &, Range[20]]

Crossrefs

Cf. A001891, A356619, A356620.

Sequence in context: A356620 A030196 A248425 * A130103 A000295 A125128

Adjacent sequences: A356618 A356619 A356620 * A356622 A356623 A356624

Keyword

nonn,easy

Author

Clark Kimberling, Sep 04 2022

Status

approved