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

1,1

Comments

Row 4 of A224524

Links

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

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

Example

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

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 *)

Crossrefs

Cf. A002541, A024917, A224524.

Sequence in context: A182171 A202435 A202428 * A251270 A255083 A063880

Adjacent sequences: A224523 A224524 A224525 * A224527 A224528 A224529

Keyword

nonn

Author

R. H. Hardin, Apr 09 2013

Extensions

More terms from Metin Sariyar, Dec 15 2019

Status

approved