cp's OEIS Frontend

A224665 T(n,k)=Number of n X n 0..k matrices with each 2X2 subblock idempotent.

%I A224665 #7 Jul 23 2025 05:17:33
%S A224665 2,3,8,4,12,32,5,16,50,78,6,20,72,108,196,7,24,98,142,260,428,8,28,
%T A224665 128,180,332,542,916,9,32,162,222,412,668,1126,1858,10,36,200,268,500,
%U A224665 806,1356,2230,3678,11,40,242,318,596,956,1606,2634,4336,7096,12,44,288,372
%N A224665 T(n,k)=Number of n X n 0..k matrices with each 2X2 subblock idempotent.
%C A224665 Table starts
%C A224665 ....2....3....4.....5.....6.....7.....8....9...10...11...12...13..14..15.16.17
%C A224665 ....8...12...16....20....24....28....32...36...40...44...48...52..56..60.64
%C A224665 ...32...50...72....98...128...162...200..242..288..338..392..450.512.578
%C A224665 ...78..108..142...180...222...268...318..372..430..492..558..628.702
%C A224665 ..196..260..332...412...500...596...700..812..932.1060.1196.1340
%C A224665 ..428..542..668...806...956..1118..1292.1478.1676.1886.2108
%C A224665 ..916.1126.1356..1606..1876..2166..2476.2806.3156.3526
%C A224665 .1858.2230.2634..3070..3538..4038..4570.5134.5730
%C A224665 .3678.4336.5046..5808..6622..7488..8406.9376
%C A224665 .7096.8246.9480.10798.12200.13686.15256
%H A224665 R. H. Hardin, <a href="/A224665/b224665.txt">Table of n, a(n) for n = 1..132</a>
%F A224665 Empirical for columns k=1..7:
%F A224665 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
%F A224665 Empirical for row n:
%F A224665 n=1: a(n) = 0*n^2 + 1*n + 1
%F A224665 n=2: a(n) = 0*n^2 + 4*n + 4
%F A224665 n=3: a(n) = 2*n^2 + 12*n + 18
%F A224665 n=4: a(n) = 2*n^2 + 24*n + 52
%F A224665 n=5: a(n) = 4*n^2 + 52*n + 140
%F A224665 n=6: a(n) = 6*n^2 + 96*n + 326
%F A224665 n=7: a(n) = 10*n^2 + 180*n + 726
%F A224665 n=8: a(n) = 16*n^2 + 324*n + 1518
%F A224665 n=9: a(n) = 26*n^2 + 580*n + 3072
%F A224665 n=10: a(n) = 42*n^2 + 1024*n + 6030
%F A224665 n=11: a(n) = 68*n^2 + 1796*n + 11594
%F A224665 n=12: a(n) = 110*n^2 + 3128*n + 21912
%e A224665 Some solutions for n=3 k=4
%e A224665 ..1..1..4....1..0..0....1..1..3....1..0..0....1..1..1....1..1..3....1..1..2
%e A224665 ..0..0..0....1..0..0....0..0..0....1..0..0....0..0..0....0..0..0....0..0..0
%e A224665 ..3..1..1....1..0..0....0..0..0....0..0..1....1..1..1....4..1..1....2..1..1
%Y A224665 Column 1 is A224543(n-1)
%Y A224665 Row 1 is A000027(n+1)
%Y A224665 Row 2 is A008574(n+1)
%Y A224665 Row 3 is A001105(n+3)
%K A224665 nonn,tabl
%O A224665 1,1
%A A224665 _R. H. Hardin_ Apr 14 2013