A224329 - OEIS

%I #8 Aug 29 2018 08:45:47

%S 1,18,147,996,6245,37494,218743,1249992,7031241,39062490,214843739,

%T 1171874988,6347656237,34179687486,183105468735,976562499984,

%U 5187988281233,27465820312482,144958496093731,762939453124980

%N Number of idempotent n X n 0..4 matrices of rank n-1.

%C Column 4 of A224333.

%H R. H. Hardin, <a href="/A224329/b224329.txt">Table of n, a(n) for n = 1..210</a>

%F a(n) = n*(2*5^(n-1)-1).

%F a(n) = 12*a(n-1) - 46*a(n-2) + 60*a(n-3) - 25*a(n-4).

%F G.f.: x*(1 + 6*x - 23*x^2) / ((1 - x)^2*(1 - 5*x)^2). - _Colin Barker_, Aug 29 2018

%e Some solutions for n=3:

%e ..0..0..0....1..0..0....0..4..2....1..0..0....1..0..0....1..0..0....1..2..0

%e ..3..1..0....0..1..2....0..1..0....1..0..3....0..1..3....0..0..0....0..0..0

%e ..3..0..1....0..0..0....0..0..1....0..0..1....0..0..0....0..0..1....0..0..1

%o (PARI) Vec(x*(1 + 6*x - 23*x^2) / ((1 - x)^2*(1 - 5*x)^2) + O(x^40)) \\ _Colin Barker_, Aug 29 2018

%Y Cf. A224333.

%K nonn,easy

%O 1,2

%A _R. H. Hardin_, formula via _M. F. Hasler_ _William J. Keith_ and Rob Pratt in the Sequence Fans Mailing List, Apr 03 2013