A224332 - OEIS

%I #16 Aug 31 2018 15:59:43

%S 1,30,381,4092,40955,393210,3670009,33554424,301989879,2684354550,

%T 23622320117,206158430196,1786706395123,15393162788850,

%U 131941395333105,1125899906842608,9570149208162287,81064793292668910,684547143360315373

%N Number of idempotent n X n 0..7 matrices of rank n-1.

%C Column 7 of A224333.

%H R. H. Hardin, <a href="/A224332/b224332.txt">Table of n, a(n) for n = 1..210</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (18,-97,144,-64).

%F a(n) = n*(2*8^(n-1)-1).

%F a(n) = 18*a(n-1) - 97*a(n-2) + 144*a(n-3) - 64*a(n-4).

%F G.f.: x*(1 + 12*x - 62*x^2) / ((1 - x)^2*(1 - 8*x)^2). - _Colin Barker_, Aug 29 2018

%e Some solutions for n=3:

%e ..1..0..3....0..0..4....0..3..0....0..0..1....1..0..6....0..7..7....1..0..3

%e ..0..1..3....0..1..0....0..1..0....0..1..0....0..1..4....0..1..0....0..1..6

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

%t Table[n*(2*8^(n-1)-1), {n, 1, 40}] (* _Stefano Spezia_, Aug 29 2018 *)

%o (PARI) Vec(x*(1 + 12*x - 62*x^2) / ((1 - x)^2*(1 - 8*x)^2) + O(x^40)) \\ _Colin Barker_, Aug 29 2018

%o (PARI) a(n) = n*(2*8^(n-1)-1); \\ _Altug Alkan_, Aug 31 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