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

0,2

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).

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

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.

Example

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;
    ...

Prog

(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) }

Crossrefs

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

Sequence in context: A324574 A143201 A340082 * A254048 A306671 A308210

Adjacent sequences: A348644 A348645 A348646 * A348648 A348649 A348650

Keyword

nonn,look,tabf

Author

Rémy Sigrist, Oct 27 2021

Status

approved