A224665 T(n,k)=Number of n X n 0..k matrices with each 2X2 subblock idempotent.
2, 3, 8, 4, 12, 32, 5, 16, 50, 78, 6, 20, 72, 108, 196, 7, 24, 98, 142, 260, 428, 8, 28, 128, 180, 332, 542, 916, 9, 32, 162, 222, 412, 668, 1126, 1858, 10, 36, 200, 268, 500, 806, 1356, 2230, 3678, 11, 40, 242, 318, 596, 956, 1606, 2634, 4336, 7096, 12, 44, 288, 372
Offset: 1
Examples
Some solutions for n=3 k=4 ..1..1..4....1..0..0....1..1..3....1..0..0....1..1..1....1..1..3....1..1..2 ..0..0..0....1..0..0....0..0..0....1..0..0....0..0..0....0..0..0....0..0..0 ..3..1..1....1..0..0....0..0..0....0..0..1....1..1..1....4..1..1....2..1..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..132
Crossrefs
Formula
Empirical for columns k=1..7:
k=1..7: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>10
Empirical for row n:
n=1: a(n) = 0*n^2 + 1*n + 1
n=2: a(n) = 0*n^2 + 4*n + 4
n=3: a(n) = 2*n^2 + 12*n + 18
n=4: a(n) = 2*n^2 + 24*n + 52
n=5: a(n) = 4*n^2 + 52*n + 140
n=6: a(n) = 6*n^2 + 96*n + 326
n=7: a(n) = 10*n^2 + 180*n + 726
n=8: a(n) = 16*n^2 + 324*n + 1518
n=9: a(n) = 26*n^2 + 580*n + 3072
n=10: a(n) = 42*n^2 + 1024*n + 6030
n=11: a(n) = 68*n^2 + 1796*n + 11594
n=12: a(n) = 110*n^2 + 3128*n + 21912
Comments