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
Examples
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; ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
- Tian-Xiao He, A-sequences, Z-sequence, and B-sequences of Riordan matrices, Discrete Mathematics 343.3 (2020): 111718. Also arXiv preprint, arXiv:1909.02639 [math.CO], 2019.
Crossrefs
Cf. A110438.
Programs
-
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
Extensions
Terms a(28) and beyond from Andrew Howroyd, Mar 02 2023