A356620 - OEIS

A356620

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) <= 4 for i = 2,...,k.

0, 1, 4, 11, 26, 56, 115, 230, 453, 884, 1716, 3321, 6416, 12383, 23886, 46060, 88803, 171194, 330009, 636136, 1226216, 2363633, 4556076, 8782147, 16928162, 32630112, 62896595, 121237118, 233692093, 450456028, 868281948, 1673667305, 3226097496, 6218502903

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..33.

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

FORMULA

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

a(n) = 3*a(n-1) - 2*a(n-2) - a(n-5) + a(n-6).

MATHEMATICA

maxDiff = 4; t = Map[Length[Select[Map[{#, Max[Differences[#]]} &,

Drop[Subsets[Range[#]], # + 1]], #[[2]] <= maxDiff &]] &, Range[18]]