A332601 An RNA-type Riordan lower-triangular matrix, read by rows.

1, 1, 1, 2, 2, 1, 4, 4, 3, 1, 8, 9, 7, 4, 1, 17, 20, 17, 11, 5, 1, 37, 45, 41, 29, 16, 6, 1, 82, 103, 98, 75, 46, 22, 7, 1, 185, 238, 235, 190, 127, 69, 29, 8, 1, 423, 555, 565, 477, 340, 203, 99, 37, 9, 1, 978, 1305, 1362, 1192, 893, 573, 310, 137, 46, 10, 1

Offset

0,4

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

He, Tian-Xiao. "A-sequences, Z-sequence, and B-sequences of Riordan matrices." Discrete Mathematics 343.3 (2020): 111718. Also arXiv:1909.02639.

Example

Triangle begins:
   1;
   1,  1;
   2,  2,  1;
   4,  4,  3,  1;
   8,  9,  7,  4,  1;
  17, 20, 17, 11,  5, 1;
  37, 45, 41, 29, 16, 6, 1;
  ...

Prog

(PARI) \\ ColGf gives the g.f. of the k-th column.
ColGf(k, n)={my(g=(1 - x + x^2 - sqrt(1 - 2*x - x^2 - 2*x^3 + x^4 + O(x^(n-k+4))))/(2*x^2)); (g - 1)/x*(x*g)^k}
T(n, k) = {polcoef(ColGf(k, n), n)} \\ Andrew Howroyd, Mar 02 2023

Crossrefs

Cf. A110438.

Sequence in context: A128175 A104040 A338131 * A348840 A182222 A225639

Adjacent sequences: A332598 A332599 A332600 * A332602 A332603 A332604

Keyword

nonn,tabl

Author

N. J. A. Sloane, Mar 06 2020

Extensions

Terms a(28) and beyond from Andrew Howroyd, Mar 02 2023

Status

approved