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A198295 Riordan array (1, x*(1+x)/(1-x^3)). 4
1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 3, 1, 0, 1, 2, 3, 4, 1, 0, 0, 4, 4, 6, 5, 1, 0, 1, 2, 9, 8, 10, 6, 1, 0, 1, 3, 9, 17, 15, 15, 7, 1, 0, 0, 6, 9, 24, 30, 26, 21, 8, 1, 0, 1, 3, 18, 26, 51, 51, 42, 28, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Triangle T(n,k), read by rows, given by (0, 1, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

Antidiagonals sums: see A159284.

REFERENCES

A. Luzón, D. Merlini, M. A. Morón, R. Sprugnoli, Complementary Riordan arrays, Discrete Applied Mathematics, 172 (2014) 75-87.

LINKS

Table of n, a(n) for n=0..65.

Milan Janjic, Binomial Coefficients and Enumeration of Restricted Words, Journal of Integer Sequences, 2016, Vol 19, #16.7.3

FORMULA

Sum_{k, 0<=k<=n} T(n,k) = A001590(n+2), n>0.

Sum_{k, 0<=k<=n}T(n,k)*(-1)^(n-k) = A078056(n-1), n>0.

T(n,n) = A000012(n), T(n+1,n) = A001477(n) = n, T(n+2,n) = A161680(n) = A000217(n-1); T(n+3,n) = A000125(n-1), n>=1.

G.f.: (-1+x)*(1+x+x^2)/(-1+x^3+x*y+x^2*y). - R. J. Mathar, Aug 11 2015

EXAMPLE

Triangle begins:

1

0, 1

0, 1, 1

0, 0, 2, 1

0, 1, 1, 3, 1

0, 1, 2, 3, 4, 1

0, 0, 4, 4, 6, 5, 1

0, 1, 2, 9, 8, 10, 6, 1

0, 1, 3, 9, 17, 15, 15, 7, 1

CROSSREFS

Cf. Columns: A000007, A011655, A186731, A185395, A185292.

Cf. Diagonals: A000012, A001477, A161680, A000125.

Sequence in context: A137560 A201093 A131255 * A221857 A133607 A103631

Adjacent sequences:  A198292 A198293 A198294 * A198296 A198297 A198298

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Jan 26 2012

STATUS

approved

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Last modified February 19 19:18 EST 2020. Contains 332047 sequences. (Running on oeis4.)