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.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

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

Adjacent sequences: A250349 A250350 A250351 * A250353 A250354 A250355

Keyword

nonn,easy

Author

R. H. Hardin, Nov 19 2014

Status

approved