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A351874
Number of subsets of {1,2,...,n} such that no two elements differ by 1, 3, or 4.
2
1, 2, 3, 5, 7, 9, 12, 16, 23, 33, 47, 66, 91, 126, 175, 245, 344, 482, 674, 940, 1311, 1830, 2557, 3575, 4997, 6982, 9752, 13620, 19025, 26579, 37136, 51885, 72487, 101264, 141463, 197624, 276088, 385711, 538860, 752810, 1051698, 1469249, 2052584, 2867532
OFFSET
0,2
FORMULA
a(n) = a(n-1) + a(n-5) + a(n-7) + delta(n,0) + delta(n,1) + delta(n,2) + 2*delta(n,3) + 2*delta(n,4) + delta(n,5) + delta(n,6), a(n<0) = 0.
G.f.: (1 + x + x^2 + 2*x^3 + 2*x^4 + x^5 + x^6)/(1 - x - x^5 - x^7).
EXAMPLE
When n = 5, the 9 subsets are {}, {1}, {2}, {3}, {4}, {5}, {1,3}, {2,4}, and {3,5}.
MATHEMATICA
CoefficientList[Series[(1 + x + x^2 + 2x^3 + 2x^4 + x^5 + x^6)/(1 - x - x^5 - x^7), {x, 0, 45}], x]
CROSSREFS
See A375981 for other sequences related to restricted combinations.
Column k=13 of A376033.
Sequence in context: A062438 A102424 A237826 * A080000 A333573 A361852
KEYWORD
easy,nonn
AUTHOR
Michael A. Allen, Feb 22 2022
STATUS
approved