|
%I #27 Feb 21 2024 08:19:45
%S 1,1,1,1,1,1,1,1,2,3,1,0,0,0,1,1,3,6,4,1,0,0,0,0,0,0,0,0,0,0,1,1,4,11,
%T 10,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,19,21,
%U 15,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Irregular triangle read by rows: T(n,k) (0 <= k <= 2^n-1) = number of binary strings of length n such that the smallest number whose binary representation is not visible in the string is k.
%C Suggested by A260273.
%H Alois P. Heinz, <a href="/A261015/b261015.txt">Rows n = 1..15, flattened</a>
%e Triangle begins:
%e 1,1,
%e 1,1,1,1,
%e 1,1,2,3,1,0,0,0,
%e 1,1,3,6,4,1,0,0,0,0,0,0,0,0,0,0,
%e ...
%e For row 3, here are the 8 strings of length 3 and for each one, the smallest missing number k:
%e 000 1
%e 001 2
%e 010 3
%e 011 2
%e 100 3
%e 101 3
%e 110 4
%e 111 0
%t notVis[bits_] := For[i = 0, True, i++, If[SequencePosition[bits, IntegerDigits[i, 2]] == {}, Return[i]]];
%t T[n_, k_] := Select[Rest[IntegerDigits[#, 2]]& /@ Range[2^n, 2^(n+1)-1], notVis[#] == k&] // Length;
%t Table[T[n, k], {n, 1, 6}, {k, 0, 2^n-1}] // Flatten (* _Jean-François Alcover_, Aug 02 2018 *)
%Y Cf. A260273, A261016, A261017.
%Y See A261019 for a more compact version (which has further information about the columns).
%K nonn,tabf
%O 1,9
%A _N. J. A. Sloane_, Aug 16 2015
%E More terms from _Alois P. Heinz_, Aug 17 2015
|
