A179808 Number of n X 3 arrays with every diagonal and antidiagonal of length L containing a permutation of 1..L.

0, 1, 4, 9, 12, 25, 60, 121, 220, 441, 924, 1849, 3612, 7225, 14620, 29241, 58140, 116281, 233244, 466489, 931612, 1863225, 3729180, 7458361, 14911260, 29822521, 59655964, 119311929, 238602012, 477204025, 954451740, 1908903481, 3817719580

Offset

3,3

Links

R. H. Hardin, Table of n, a(n) for n=3..99

Formula

Empirical: a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)+2*a(n-4)-4*a(n-5); G.f.: -(-x-2*x^2-2*x^3+4*x^4)*x^3 / (1-2*x+x^2-2*x^3-2*x^4+4*x^5).

Example

All solutions for 5 X 3:
.1.1.1...1.1.1...1.2.1...1.2.1
.2.2.2...2.3.2...1.3.1...1.2.1
.3.3.3...2.3.2...2.3.2...3.3.3
.1.2.1...1.3.1...2.3.2...2.2.2
.1.2.1...1.2.1...1.1.1...1.1.1

Crossrefs

Sequence in context: A254520 A344578 A283105 * A083351 A055381 A287498

Adjacent sequences: A179805 A179806 A179807 * A179809 A179810 A179811

Keyword

nonn

Author

R. H. Hardin, formula from Alois P. Heinz in the Sequence Fans Mailing List, Jul 28 2010

Status

approved