%I A121547
%S A121547 0,0,1,0,4,4,0,10,20,10,0,20,60,60,20,0,35,140,210,140,35,0,56,280,560,
%T A121547 560,280,56,0,84,504,1260,1680,1260,504,84,0,120,840,2520,4200,4200,
%U A121547 2520,840,120,0,165,1320,4620,9240,11550,9240,4620,1320,165,1980,7920
%N A121547 Fourth slice along the 1-2-plane in the cube a(m,n,o) = a(m-1,n,o)+a(m,
               n-1,o)+a(m,n,o-1) for which the first slice is Pascal's triangle 
               (slice read by anti-diagonals).
%H A121547 Thomas Wieder, <a href="http://www.thomas-wieder.privat.t-online.de/">
               Home Page</a>.
%H A121547 Thomas Wieder, <a href="http://homepages.tu-darmstadt.de/~wieder">(Old) 
               Home Page</a>.
%F A121547 a(m-1,n,o)+a(m,n-1,o)+a(m,n,o-1) with initialization values a(1,0,0)=1 
               and a(m<>1=0,n>=0,0>=o)=0.
%e A121547 The second row is 1,4,10,20,35,56,84,120,165,220 = A000292 Tetrahedral 
               (or pyramidal) numbers: C(n+2,3) = n(n+1)(n+2)/6 (core).
%e A121547 The third row is 4,20,60,140,280,504,840,1320,1980,2860 = A033488 = n*(n+1)*(n+2)*(n+3)/
               6.
%e A121547 The main diagonal is 0,4,60,560,4200,27720,168168,960960,5250960,27713400 
               = unknown.
%o A121547 Excel cell formula: =ZS(-1)+Z(-1)S+Z(-15)S where the term Z(-15)S refers 
               to a cell in the previous slice (along the dimension 3), i.e. Z(-15)S 
               corresponds to +a(m,n,o-1).
%Y A121547 Cf. A003506, A094305, A121306, A119800, A000292, A007318.
%Y A121547 Sequence in context: A129507 A165727 A021698 this_sequence A028626 A137862 
               A006805
%Y A121547 Adjacent sequences: A121544 A121545 A121546 this_sequence A121548 A121549 
               A121550
%K A121547 nonn,tabl
%O A121547 0,5
%A A121547 Thomas Wieder (thomas.wieder(AT)t-online.de), Aug 06 2006