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A177994
Triangle read by rows, A177990 * A070909
6
1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 5, 1, 4, 1, 3, 1, 2, 1, 1, 5, 1, 4, 1, 3, 1, 2, 1, 1, 1
OFFSET
0,4
COMMENTS
Row sums = A101881: (1, 2, 4, 5, 8, 9, 13, 14,...).
Double Riordan array ( 1/((1 - x)*(1 - x^2)); x*(1 - x^2), x/(1 - x^2) ) as defined in Davenport et al. The set of double Riordan arrays of the form ( g(x); x*f_1(x), x*f_2(x) ), where f_1(x)*f_2(x) = 1, forms a group under matrix multiplication. Here g, f_1 and f_2 denote power series with constant term equal to 1. This is the array (( 1/((1 - x)*(1 - x^2)), 1/(1 - x) )) in the notation of the Bala link. - Peter Bala, Aug 26 2021
LINKS
D. E. Davenport, L. W. Shapiro and L. C. Woodson, The Double Riordan Group, The Electronic Journal of Combinatorics, 18(2) (2012).
FORMULA
As infinite lower triangular matrices, A177990 * A070909
EXAMPLE
First few rows of the triangle =
1;
1, 1;
2, 1, 1;
2, 1, 1, 1;
3, 1, 2, 1, 1;
3, 1, 2, 1, 1, 1;
4, 1, 3, 1, 2, 1, 1;
4, 1, 3, 1, 2, 1, 1, 1;
5, 1, 4, 1, 3, 1, 2, 1, 1;
5, 1, 4, 1, 3, 1, 2, 1, 1, 1;
6, 1, 5, 1, 4, 1, 3, 1, 2, 1, 1;
6, 1, 5, 1, 4, 1, 3, 1, 2, 1, 1, 1;
7, 1, 6, 1, 5, 1, 4, 1, 3, 1, 2, 1, 1;
7, 1, 6, 1, 5, 1, 4, 1, 3, 1, 2, 1, 1, 1;
...
PROG
(Haskell)
a177994 n k = a177994_tabl !! n !! k
a177994_row n = a177994_tabl !! n
a177994_tabl = [1] : [1, 1] : map f a177994_tabl
where f xs@(x:_) = (x + 1) : 1 : xs
-- Reinhard Zumkeller, Feb 20 2015
CROSSREFS
Cf. A101881.
Sequence in context: A376612 A306722 A168508 * A179285 A079211 A026835
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, May 16 2010
STATUS
approved