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

108, 404, 892, 1716, 2732, 4324, 6060, 8516, 11308, 14820, 18572, 23668, 28716, 34916, 41836, 49860, 58076, 68164, 78252, 90356, 102988, 116868, 131276, 148564, 165660, 184532, 204604, 226788, 249116, 274900, 300252, 328628, 357868, 389028, 421580, 457924, 493500

Offset: 1

Author

R. H. Hardin, Apr 09 2013

Keywords

• nonn

Comments

Row 4 of A224524

Examples

			Some solutions for n=3:
  0 0 0 0     0 0 0 0     1 0 0 0     0 0 0 0     0 0 0 0
  0 0 0 0     2 0 0 1     0 0 0 0     1 1 0 0     0 0 0 0
  2 0 1 0     2 0 0 1     0 0 0 0     3 3 0 0     0 0 0 0
  0 0 0 0     2 0 0 1     0 0 0 0     2 2 0 0     1 0 1 1
		

Links

• Robert Israel, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A002541, A024917, A224524.

Programs

Maple

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:
map(F4, [$1..100]); # Robert Israel, Dec 15 2019

Mathematica

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 *)

Formula

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

Extensions

More terms from Metin Sariyar, Dec 15 2019