A139687 Basis of degenerate cases of sequences identical to its p-th differences. Complement to A140344 which is based on natural Catalan's triangle. Triangle without first term (probable 1) on line.

1, 1, 1, 2, 2, 1, 3, 5, 5, 1, 3, 6, 9, 9, 1, 4, 10, 19, 28, 28, 1, 4, 10, 20, 34, 48, 48, 1, 5, 15, 35, 69, 117, 165, 165, 1, 5, 15, 35, 70, 125, 200, 275, 275, 1, 6, 21, 56, 126, 251, 451, 726, 1001, 1001, 1, 6, 21, 56, 126, 252, 461, 780, 1209, 1638, 1638

Offset

0,4

Comments

Triangle from A140344:

(1;)

0, 1, 1;

0, 0, 1, 2, 2;

0, 0, 0, 1, 3, 5, 5; see A138112,

0, 0, 0, 0, 1, 4, 9, 14, 14; see A140343,

begins (without 0's) like a(n).

Links

Table of n, a(n) for n=0..64.

Formula

First four rows of triangle from second row: 1, 1; 1, 2, 2; see A099087, 1, 3, 5, 5; 1, 3, 6, 9, 9; see A057083 which can be preceded with 3 leading 0's, are, as said, from natural Catalan's triangle A009766. Origin of a(n) explained later.

Crossrefs

Cf. A135356, A140344.

Sequence in context: A349414 A257006 A363565 * A188181 A064581 A064580

Adjacent sequences: A139684 A139685 A139686 * A139688 A139689 A139690

Keyword

nonn,uned

Author

Paul Curtz, Jun 13 2008

Status

approved