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An RNA-type Riordan lower-triangular matrix, read by rows.
1

%I #12 Aug 05 2024 05:26:38

%S 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,

%T 103,98,75,46,22,7,1,185,238,235,190,127,69,29,8,1,423,555,565,477,

%U 340,203,99,37,9,1,978,1305,1362,1192,893,573,310,137,46,10,1

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

%H Andrew Howroyd, <a href="/A332601/b332601.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)

%H He, Tian-Xiao. "A-sequences, Z-sequence, and B-sequences of Riordan matrices." Discrete Mathematics 343.3 (2020): 111718. Also <a href="https://arxiv.org/abs/1909.02639">arXiv:1909.02639</a>.

%e Triangle begins:

%e 1;

%e 1, 1;

%e 2, 2, 1;

%e 4, 4, 3, 1;

%e 8, 9, 7, 4, 1;

%e 17, 20, 17, 11, 5, 1;

%e 37, 45, 41, 29, 16, 6, 1;

%e ...

%o (PARI) \\ ColGf gives the g.f. of the k-th column.

%o 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}

%o T(n,k) = {polcoef(ColGf(k,n), n)} \\ _Andrew Howroyd_, Mar 02 2023

%Y Cf. A110438.

%K nonn,tabl

%O 0,4

%A _N. J. A. Sloane_, Mar 06 2020

%E Terms a(28) and beyond from _Andrew Howroyd_, Mar 02 2023