A250352 - OEIS

%I #18 Sep 03 2023 18:21:18

%S 8,26,62,122,212,338,506,722,992,1322,1718,2186,2732,3362,4082,4898,

%T 5816,6842,7982,9242,10628,12146,13802,15602,17552,19658,21926,24362,

%U 26972,29762,32738,35906,39272,42842,46622,50618,54836,59282,63962,68882,74048

%N 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.

%C 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

%H R. H. Hardin, <a href="/A250352/b250352.txt">Table of n, a(n) for n = 1..210</a>

%H N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, <a href="https://vimeo.com/314786942">Part I</a>, <a href="https://vimeo.com/314790822">Part 2</a>, <a href="https://oeis.org/A320487/a320487.pdf">Slides</a>. (Mentions this sequence)

%F a(n) = n^3 + 3*n^2 + 2*n + 2 = 2*A158842(n+1).

%F From _Colin Barker_, Nov 12 2018: (Start)

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

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

%F (End)

%e Some solutions for n=6:

%e   2  0  1  2  6  4  0  1  0  0  2  4  6  2  4  0

%e   4  4  7  7  2  4  2  3  1  6  1  2  3  6  5  5

%e   6  4  7  2  4  7  8  5  3  6  4  7  5  8  8  2

%Y Row 3 of A250351.

%K nonn,easy

%O 1,1

%A _R. H. Hardin_, Nov 19 2014