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 A224665 T(n,k)=Number of n X n 0..k matrices with each 2X2 subblock idempotent 10
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ....2....3....4.....5.....6.....7.....8....9...10...11...12...13..14..15.16.17 ....8...12...16....20....24....28....32...36...40...44...48...52..56..60.64 ...32...50...72....98...128...162...200..242..288..338..392..450.512.578 ...78..108..142...180...222...268...318..372..430..492..558..628.702 ..196..260..332...412...500...596...700..812..932.1060.1196.1340 ..428..542..668...806...956..1118..1292.1478.1676.1886.2108 ..916.1126.1356..1606..1876..2166..2476.2806.3156.3526 .1858.2230.2634..3070..3538..4038..4570.5134.5730 .3678.4336.5046..5808..6622..7488..8406.9376 .7096.8246.9480.10798.12200.13686.15256 LINKS R. H. Hardin, Table of n, a(n) for n = 1..132 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 EXAMPLE 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 CROSSREFS Column 1 is A224543(n-1) Row 1 is A000027(n+1) Row 2 is A008574(n+1) Row 3 is A001105(n+3) Sequence in context: A198369 A193731 A193975 * A098514 A161198 A195232 Adjacent sequences:  A224662 A224663 A224664 * A224666 A224667 A224668 KEYWORD nonn,tabl AUTHOR R. H. Hardin Apr 14 2013 STATUS approved

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Last modified November 27 12:51 EST 2021. Contains 349394 sequences. (Running on oeis4.)