cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A166830 Number of n X 3 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nonincreasing order.

Original entry on oeis.org

2, 8, 18, 33, 54, 82, 118, 163, 218, 284, 362, 453, 558, 678, 814, 967, 1138, 1328, 1538, 1769, 2022, 2298, 2598, 2923, 3274, 3652, 4058, 4493, 4958, 5454, 5982, 6543, 7138, 7768, 8434, 9137, 9878, 10658, 11478, 12339, 13242
Offset: 1

Views

Author

R. H. Hardin, Oct 21 2009

Keywords

Examples

			All solutions for n=3
...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1
...1.1.1...1.1.1...1.1.1...2.1.1...2.1.1...2.1.1...2.2.1...2.2.1...2.2.2
...2.1.1...2.2.1...2.2.2...2.1.1...2.2.1...2.2.2...2.2.1...2.2.2...2.2.2
------
...2.1.1...2.1.1...2.1.1...2.1.1...2.1.1...2.1.1...2.2.1...2.2.1...2.2.1
...2.1.1...2.1.1...2.1.1...2.2.1...2.2.1...2.2.2...2.2.1...2.2.1...2.2.2
...2.1.1...2.2.1...2.2.2...2.2.1...2.2.2...2.2.2...2.2.1...2.2.2...2.2.2
		

Programs

Formula

Empirical: a(n) = (n^3+6*n^2+11*n-6)/6.
a(n) = A167772(n+3,n). - Philippe Deléham, Nov 11 2009
a(n) = A227819(n+6,n+2). - Alois P. Heinz, Sep 22 2013
Empirical: a(n) = floor(A000292(n+1)^3/(A000292(n+1) + 1)^ 2). - Ivan N. Ianakiev, Nov 05 2013
From G. C. Greubel, May 25 2016: (Start)
Empirical G.f.: (-1 + 6*x - 6*x^2 + 2*x^3)/(1 - x)^4 + 1.
Empirical E.g.f.: (1/6)*(-6 + 18*x + 9*x^2 + x^3)*exp(x) + 1. (End)