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A214326 Square array read by antidiagonals in which T(n,b) gives the n-th Fibonacci number written in base b with n,b >= 1.

%I A214326 #47 Sep 12 2018 16:47:28
%S A214326 1,1,1,1,1,11,1,1,10,111,1,1,2,11,11111,1,1,2,10,101,11111111,1,1,2,3,
%T A214326 12,1000,1111111111111,1,1,2,3,11,22,1101,111111111111111111111,1,1,2,
%U A214326 3,10,20,111,10101,1111111111111111111111111111111111,1,1,2,3,5,13,31,210,100010
%N A214326 Square array read by antidiagonals in which T(n,b) gives the n-th Fibonacci number written in base b with n,b >= 1.
%C A214326 For b > 10, some terms cannot be properly notated using only decimal characters.
%H A214326 Alois P. Heinz, <a href="/A214326/b214326.txt">Antidiagonals n = 1..13</a>
%e A214326 Square array A(n,b) begins:
%e A214326               1,    1,   1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...
%e A214326               1,    1,   1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...
%e A214326              11,   10,   2,  2,  2,  2,  2,  2,  2,  2,  2,  2, ...
%e A214326             111,   11,  10,  3,  3,  3,  3,  3,  3,  3,  3,  3, ...
%e A214326           11111,  101,  12, 11, 10,  5,  5,  5,  5,  5,  5,  5, ...
%e A214326        11111111, 1000,  22, 20, 13, 12, 11, 10,  8,  8,  8,  8, ...
%e A214326   1111111111111, 1101, 111, 31, 23, 21, 16, 15, 14, 13, 12, 11, ...
%p A214326 A:= proc(n, b) local f, l; f:= combinat[fibonacci](n);
%p A214326       if b=1 then parse(cat(1$f))
%p A214326     else l:= NULL;
%p A214326          while f>0 do l:= irem(f, b, 'f'), l od;
%p A214326          parse(cat(l))
%p A214326       fi
%p A214326     end:
%p A214326 seq(seq(A(n, 1+d-n), n=1..d), d=1..10);
%Y A214326 Columns b=1-10, 12, 13 give: A108047, A004685, A004686, A004687, A004688, A004689, A004690, A004691, A004692, A000045, A004693, A004694.
%Y A214326 Cf. A037842, A131293.
%K A214326 nonn,tabl,easy,base
%O A214326 1,6
%A A214326 _Alois P. Heinz_, Jul 24 2012