A348647 Irregular table read by rows; the n-th row contains the lengths of the runs of consecutive terms with the same parity in the n-th row of Pascal's triangle (A007318).

1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 8, 1, 7, 1, 2, 6, 2, 1, 1, 1, 5, 1, 1, 1, 4, 4, 4, 1, 3, 1, 3, 1, 3, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16, 1, 15, 1, 2, 14, 2, 1, 1, 1, 13, 1, 1, 1, 4, 12, 4, 1, 3, 1, 11, 1, 3, 1

Offset: 0

Author

Rémy Sigrist, Oct 27 2021

Keywords

• nonn
• look
• tabf

Comments

For any n >= 0, the n-th row:

- is palindromic,

- has A038573(n+1) terms,

- has leading term A006519(n+1),

- has central term A080079(n+1).

Examples

			Triangle begins:
    1;
    2;
    1, 1, 1;
    4;
    1, 3, 1;
    2, 2, 2;
    1, 1, 1, 1, 1, 1, 1;
    8;
    1, 7, 1;
    2, 6, 2;
    1, 1, 1, 5, 1, 1, 1;
    4, 4, 4;
    1, 3, 1, 3, 1, 3, 1;
    2, 2, 2, 2, 2, 2, 2;
    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
    16;
    ...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6304 (rows for n = 0..254, flattened)
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

Cf. A006519, A007318, A038573, A047999, A048896, A080079.

Programs

PARI

row(n) = { my (b=binomial(n)%2, r=[], p=1, w=1); for (k=2, #b, if (p==b[k], w++, r=concat(r, w); p=b[k]; w=1)); concat(r, w) }

Formula

Sum_{k = 1..A038573(n+1)} T(n, k) = n+1.

T(n, 1) = A006519(n+1).

T(n, A048896(n)) = A080079(n+1).

T(2^k-1, 1) = 2^k for any k >= 0.