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A250352
Number of length 3 arrays x(i), i=1..3 with x(i) in i..i+n and no value appearing more than 2 times.
2
8, 26, 62, 122, 212, 338, 506, 722, 992, 1322, 1718, 2186, 2732, 3362, 4082, 4898, 5816, 6842, 7982, 9242, 10628, 12146, 13802, 15602, 17552, 19658, 21926, 24362, 26972, 29762, 32738, 35906, 39272, 42842, 46622, 50618, 54836, 59282, 63962, 68882, 74048
OFFSET
1,1
COMMENTS
a(n) = (n+1)^3 - (n-1), where (n+1)^3 is the number of ways of selecting a triple from n+1 numbers in these subintervals, and there are n-1 of these triples, (3,3,3) up to (n-2,n-2,n-2), where all values are the same, which are discarded. - R. J. Mathar, Oct 09 2020
LINKS
N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, Part I, Part 2, Slides. (Mentions this sequence)
FORMULA
a(n) = n^3 + 3*n^2 + 2*n + 2 = 2*A158842(n+1).
From Colin Barker, Nov 12 2018: (Start)
G.f.: 2*x*(4 - 3*x + 3*x^2 - x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
EXAMPLE
Some solutions for n=6:
2 0 1 2 6 4 0 1 0 0 2 4 6 2 4 0
4 4 7 7 2 4 2 3 1 6 1 2 3 6 5 5
6 4 7 2 4 7 8 5 3 6 4 7 5 8 8 2
CROSSREFS
Row 3 of A250351.
Sequence in context: A363288 A252870 A163121 * A213039 A211640 A002901
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Nov 19 2014
STATUS
approved