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 A214595 T(n,k)=Number of nXnXn triangular 0..k arrays with every horizontal row having the same average value 12
 2, 3, 2, 4, 5, 2, 5, 8, 23, 2, 6, 13, 62, 401, 2, 7, 18, 157, 1862, 20351, 2, 8, 25, 312, 10177, 187862, 2869211, 2, 9, 32, 601, 33352, 3330677, 63120962, 1127599139, 2, 10, 41, 986, 103651, 20608352, 5495329427, 71200442882, 1248252244661, 2, 11, 50, 1619 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts .2.....3......4.......5........6.........7.........8..........9.........10 .2.....5......8......13.......18........25........32.........41.........50 .2....23.....62.....157......312.......601.......986.......1619.......2426 .2...401...1862...10177....33352....103651....250042.....589763....1199614 .2.20351.187862.3330677.20608352.121537201.493575042.1877543213.5767190924 LINKS R. H. Hardin, Table of n, a(n) for n = 1..1475 FORMULA Empirical for row n: n=1: a(k)=2*a(k-1)-a(k-2) n=2: a(k)=2*a(k-1)-2*a(k-3)+a(k-4) n=3: (order 12 antisymmetric) n=4: (order 32 symmetric) n=5: (order 84 symmetric) EXAMPLE Some solutions for n=4 k=4 .....2........1........2........2........2........2........2........2 ....3.1......0.2......2.2......3.1......2.2......1.3......4.0......4.0 ...3.2.1....0.3.0....3.2.1....2.4.0....0.2.4....3.0.3....1.2.3....4.0.2 ..2.2.3.1..2.1.0.1..1.2.4.1..4.2.2.0..1.4.3.0..4.0.2.2..3.2.3.0..4.0.4.0 CROSSREFS Row 2 is A000982(n+1) Sequence in context: A226208 A304743 A214540 * A029638 A136181 A265110 Adjacent sequences:  A214592 A214593 A214594 * A214596 A214597 A214598 KEYWORD nonn,tabl AUTHOR R. H. Hardin Jul 22 2012 STATUS approved

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Last modified January 25 07:29 EST 2020. Contains 331241 sequences. (Running on oeis4.)