A238731 - OEIS

A238731

Riordan array ((1-2*x)/(1-3*x+x^2), x/(1-3*x+x^2)).

1, 1, 1, 2, 4, 1, 5, 13, 7, 1, 13, 40, 33, 10, 1, 34, 120, 132, 62, 13, 1, 89, 354, 483, 308, 100, 16, 1, 233, 1031, 1671, 1345, 595, 147, 19, 1, 610, 2972, 5561, 5398, 3030, 1020, 203, 22, 1, 1597, 8495, 17984, 20410, 13893, 5943, 1610, 268, 25, 1, 4181

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OFFSET

0,4

COMMENTS

Unsigned version of A124037 and A126126.

Subtriangle of the triangle given by (0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

Row sums are A001075(n).

Diagonal sums are A133494(n).

Sum_{k=0..n} T(n,k)*x^k = A001519(n), A001075(n), A002320(n), A038723(n), A033889(n) for x = 0, 1, 2, 3, 4 respectively. - Philippe Deléham, Mar 05 2014

LINKS

Table of n, a(n) for n=0..55.

FORMULA

T(n,k) = 3*T(n-1,k) + T(n-1,k-1) - T(n-2,k), T(0,0) = T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n.

G.f.: (1-2*x)/(1-(y+3)*x+x^2). - Philippe Deléham, Mar 05 2014

EXAMPLE

Triangle begins:

1, 1;

2, 4, 1;

5, 13, 7, 1;

13, 40, 33, 10, 1;

34, 120, 132, 62, 13, 1;