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.

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

Alois P. Heinz, Rows n = 1..15, flattened

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

Cf. A260273, A261016, A261017.

See A261019 for a more compact version (which has further information about the columns).

Sequence in context: A345752 A070078 A054438 * A286584 A174947 A010341

Adjacent sequences: A261012 A261013 A261014 * A261016 A261017 A261018

Keyword

nonn,tabf

Author

N. J. A. Sloane, Aug 16 2015

Extensions

More terms from Alois P. Heinz, Aug 17 2015

Status

approved