cp's OEIS Frontend

A224526 Number of idempotent 4 X 4 0..n matrices of rank 1.

%I A224526 #13 Dec 15 2019 21:56:51
%S A224526 108,404,892,1716,2732,4324,6060,8516,11308,14820,18572,23668,28716,
%T A224526 34916,41836,49860,58076,68164,78252,90356,102988,116868,131276,
%U A224526 148564,165660,184532,204604,226788,249116,274900,300252,328628,357868,389028,421580,457924,493500
%N A224526 Number of idempotent 4 X 4 0..n matrices of rank 1.
%C A224526 Row 4 of A224524
%H A224526 Robert Israel, <a href="/A224526/b224526.txt">Table of n, a(n) for n = 1..4000</a>
%F A224526 a(n) = 8*n^3 + 36*n^2 + 60*n + 4 + 24*A024917(n) + 12*A002541(n) + 12*Sum_{m=2..n} floor(n/m)^2. - _Robert Israel_, Dec 15 2019
%e A224526 Some solutions for n=3:
%e A224526   0 0 0 0     0 0 0 0     1 0 0 0     0 0 0 0     0 0 0 0
%e A224526   0 0 0 0     2 0 0 1     0 0 0 0     1 1 0 0     0 0 0 0
%e A224526   2 0 1 0     2 0 0 1     0 0 0 0     3 3 0 0     0 0 0 0
%e A224526   0 0 0 0     2 0 0 1     0 0 0 0     2 2 0 0     1 0 1 1
%p A224526 F4 := k -> 8*k^3 + 36*k^2 + 24*add(m*floor(k/m), m = 2 .. k) + 12*add(floor(k/m), m = 2 .. k) + 12*add(floor(k/m)^2, m = 2 .. k) + 60*k + 4:
%p A224526 map(F4, [$1..100]); # _Robert Israel_, Dec 15 2019
%t A224526 Table[8*n^3+36*n^2+60*n+4+24*Sum[k*Floor[n/k],{k, 2, n}]+12*Sum[Floor[(n-k)/k],{k, n-1}]+12*Sum[Floor[(n/k)]^2,{k,2,n}],{n,1,100}] (* _Metin Sariyar_, Dec 15 2019 *)
%Y A224526 Cf. A002541, A024917, A224524.
%K A224526 nonn
%O A224526 1,1
%A A224526 _R. H. Hardin_, Apr 09 2013
%E A224526 More terms from _Metin Sariyar_, Dec 15 2019