A279026 Size of blocks of 1's in the second column of Catalan numbers written in binary and left-aligned.

1, 1, 2, 4, 6, 10, 15, 23, 36, 59, 93, 148, 234, 372, 592, 939, 1490, 2366, 3754, 5959, 9460, 15017, 23838, 37841, 60068, 95352, 151362

Offset

1,3

Comments

What combinatorial problem is this the answer to? - N. J. A. Sloane, Dec 21 2016

Appears to be strictly increasing for n > 1. - Chai Wah Wu, Dec 22 2016

Links

Table of n, a(n) for n=1..27.

Example

Left-align the binary representation of the Catalan numbers:
1
1
10
101
1110
101010
10000100
110101101
10110010110
The first column is all 1's, by definition.
The next column appears to have blocks of 1's and 0's.
The sizes of the blocks make this sequence.
The values of this column may be generated with the MMA code:
Table[If[2^Floor[Log2[CatalanNumber[n]]] + 2^(Floor[Log2[CatalanNumber[n]]] - 1) < CatalanNumber[n], 1, 0], {n, 1, 1000}].

Mathematica

Num = 10000;
T = Table[If[2^Floor[Log2[CatalanNumber[n]]] +2^(Floor[Log2[CatalanNumber[n]]] - 1) < CatalanNumber[n], 1, 0], {n, 1, Num}]; S = {};
For[i = 1, i < Num, i++, j = 0; If[T[[i]] == 1, While[T[[i]] == 1, i++; j++]; AppendTo[S, j]; ]; ]; S

Crossrefs

Cf. A000108.

Sequence in context: A309173 A116084 A108925 * A120549 A167270 A355108

Adjacent sequences: A279023 A279024 A279025 * A279027 A279028 A279029

Keyword

nonn,base

Author

Benedict W. J. Irwin, Dec 12 2016

Extensions

a(21)-a(27) from Chai Wah Wu, Dec 22 2016

Status

approved