A210636 - OEIS

%I #8 Feb 22 2013 14:40:35

%S 1,1,1,3,4,1,7,13,7,1,17,40,32,10,1,41,117,124,60,13,1,99,332,437,286,

%T 97,16,1,239,921,1447,1193,553,143,19,1,577,2512,4584,4556,2682,952,

%U 198,22,1,1393,6761,14048,16336,11666,5282,1510,262,25,1

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

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

%C Product of A122542 and A007318 (Pascal's triangle) as lower triangular matrices .

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

%F G.f.: (1-x)/(1-2*x-y*x-x^2-y*x^2).

%F Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A001333(n), A104934(n), A122958(n), A122690(n), A091928(n) for x = -1, 0, 1, 2, 3, 4 respectively.

%e Triangle begins :

%e 1

%e 1, 1

%e 3, 4, 1

%e 7, 13, 7, 1

%e 17, 40, 32, 10, 1

%e 41, 117, 124, 60, 13, 1

%e 99, 332, 437, 286, 97, 16, 1

%e 239, 921, 1447, 1193, 553, 143, 19, 1

%e 577, 2512, 4584, 4556, 2682, 952, 198, 22, 1

%e 1393, 6761, 14048, 16336, 11666, 5282, 1510, 262, 25, 1

%Y Cf. Columns :A001333, A119915, Diagonals : A000012, A016777, Antidiagonal sums : A077995

%K easy,nonn,tabl

%O 0,4

%A _Philippe Deléham_, Mar 26 2012