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A261015
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.
5
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, 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, 15, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
1,9
COMMENTS
Suggested by A260273.
LINKS
EXAMPLE
Triangle begins:
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,
...
For row 3, here are the 8 strings of length 3 and for each one, the smallest missing number k:
000 1
001 2
010 3
011 2
100 3
101 3
110 4
111 0
MATHEMATICA
notVis[bits_] := For[i = 0, True, i++, If[SequencePosition[bits, IntegerDigits[i, 2]] == {}, Return[i]]];
T[n_, k_] := Select[Rest[IntegerDigits[#, 2]]& /@ Range[2^n, 2^(n+1)-1], notVis[#] == k&] // Length;
Table[T[n, k], {n, 1, 6}, {k, 0, 2^n-1}] // Flatten (* Jean-François Alcover, Aug 02 2018 *)
CROSSREFS
See A261019 for a more compact version (which has further information about the columns).
Sequence in context: A345752 A070078 A054438 * A374849 A286584 A174947
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Aug 16 2015
EXTENSIONS
More terms from Alois P. Heinz, Aug 17 2015
STATUS
approved