Search: id:A028412
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%I A028412
%S A028412 1,1,1,1,3,2,1,4,8,3,1,7,17,21,5,1,11,48,72,55,8,1,18,122,329,305,144,
%T A028412 13,1,29,323,1353,2255,1292,377,21,1,47,842,5796,15005,15456,5473,987,
%U A028412 34,1,76,2208,24447,104005,166408,105937,23184,2584,55,1,123,5777
%N A028412 Rectangular array of numbers Fibonacci(m(n+1))/Fibonacci(m), m>=1, n>
               =0, read by antidiagonals.
%C A028412 Every integer-valued quotient of two Fibonacci numbers is in this array. 
               [From Clark Kimberling (ck6(AT)evansville.edu), Aug 28 2008]
%D A028412 A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of 
               combinatorial proof, M.A.A. 2003, id. 142.
%D A028412 I. Strazdins, Lucas factors and a Fibonomial generating function, in 
               Applications of Fibonacci numbers, Vol. 7 (Graz, 1996), 401-404, 
               Kluwer Acad. Publ., Dordrecht, 1998.
%F A028412 T(n, m) = Sum[i_1>=0, Sum[i_2>=0, ... Sum[i_m>=0, C(n-i_m, i_1)*C(n-i_1, 
               i_2)*C(n-i_2, i_3)*...*C(n-i_{m-1}, i_m) ] ... ]].
%e A028412 1,1,1,1,1,1,...
%e A028412 1,3,4,7,11,18,...
%e A028412 2,8,17,48,122,323,...
%e A028412 3,21,72,329,1353,5796,...
%e A028412 5,55,305,2255,15005,104005,...
%e A028412 8,144,1292,15456,166408,1866294,...
%e A028412 13,377,5473,105937,1845493,33489287,...
%e A028412 ...
%Y A028412 Columns include A000045, A001906, A001076, A004187, A049666, A049660, 
               A049667, A049668, A049669, A049670. Rows include (essentially) A000032, 
               A047946, A083564, A103226. Main diagonal is A051294.
%Y A028412 Sequence in context: A092486 A159966 A119263 this_sequence A156699 A077819 
               A030313
%Y A028412 Adjacent sequences: A028409 A028410 A028411 this_sequence A028413 A028414 
               A028415
%K A028412 tabl,nonn,easy,nice
%O A028412 0,5
%A A028412 N. J. A. Sloane (njas(AT)research.att.com).
%E A028412 More terms from Erich Friedman (efriedma(AT)stetson.edu), Jun 03 2001
%E A028412 Edited by Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 03 2005
%E A028412 Better description from Clark Kimberling, Aug 28 2008

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