# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a214595 Showing 1-1 of 1 %I A214595 #4 Jul 22 2012 07:44:36 %S A214595 2,3,2,4,5,2,5,8,23,2,6,13,62,401,2,7,18,157,1862,20351,2,8,25,312, %T A214595 10177,187862,2869211,2,9,32,601,33352,3330677,63120962,1127599139,2, %U A214595 10,41,986,103651,20608352,5495329427,71200442882,1248252244661,2,11,50,1619 %N A214595 T(n,k)=Number of nXnXn triangular 0..k arrays with every horizontal row having the same average value %C A214595 Table starts %C A214595 .2.....3......4.......5........6.........7.........8..........9.........10 %C A214595 .2.....5......8......13.......18........25........32.........41.........50 %C A214595 .2....23.....62.....157......312.......601.......986.......1619.......2426 %C A214595 .2...401...1862...10177....33352....103651....250042.....589763....1199614 %C A214595 .2.20351.187862.3330677.20608352.121537201.493575042.1877543213.5767190924 %H A214595 R. H. Hardin, Table of n, a(n) for n = 1..1475 %F A214595 Empirical for row n: %F A214595 n=1: a(k)=2*a(k-1)-a(k-2) %F A214595 n=2: a(k)=2*a(k-1)-2*a(k-3)+a(k-4) %F A214595 n=3: (order 12 antisymmetric) %F A214595 n=4: (order 32 symmetric) %F A214595 n=5: (order 84 symmetric) %e A214595 Some solutions for n=4 k=4 %e A214595 .....2........1........2........2........2........2........2........2 %e A214595 ....3.1......0.2......2.2......3.1......2.2......1.3......4.0......4.0 %e A214595 ...3.2.1....0.3.0....3.2.1....2.4.0....0.2.4....3.0.3....1.2.3....4.0.2 %e A214595 ..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 %Y A214595 Row 2 is A000982(n+1) %K A214595 nonn,tabl %O A214595 1,1 %A A214595 _R. H. Hardin_ Jul 22 2012 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE