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A224526 Number of idempotent 4 X 4 0..n matrices of rank 1. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 24 11:28 EST 2022. Contains 350534 sequences. (Running on oeis4.)