A112883 - OEIS

%I #11 Jan 26 2020 20:11:30

%S 1,0,1,0,1,3,0,0,2,5,0,0,1,7,11,0,0,0,3,16,21,0,0,0,1,12,41,43,0,0,0,

%T 0,4,34,94,85,0,0,0,0,1,18,99,219,171,0,0,0,0,0,5,60,261,492,341,0,0,

%U 0,0,0,1,25,195,678,1101,683,0,0,0,0,0,0,6,95,576,1692,2426,1365,0,0,0,0,0

%N A skew Jacobsthal-Pascal matrix.

%C T(n,n) is A001045(n), row sums are A006130, column sums are A002605. Compare with [0,1,-1,0,0,..] DELTA [1,2,-2,0,0,...] where DELTA is the operator defined in A084938. A skewed version of the Riordan array (1/(1-x-2x^2),x/(1-x-2x^2)) (A073370).

%C Modulo 2, this sequence gives A106344. - _Philippe Deléham_, Dec 18 2008

%F From _Philippe Deléham_: (Start)

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

%F Number triangle T(n, k) = Sum_{j=0..2k-n} C(n-k+j, n-k)*C(j, 2k-n-j)*2^(2k-n-j);

%F T(n, k) = A073370(k, n-k); T(n, k) = T(n-1, k-1) + T(n-2, k-1) + 2*T(n-2, k-2). (End)

%e Rows begin

%e   1;

%e   0, 1;

%e   0, 1, 3;

%e   0, 0, 2, 5;

%e   0, 0, 1, 7, 11;

%e   0, 0, 0, 3, 16, 21;

%e   0, 0, 0, 1, 12, 41, 43;

%e   0, 0, 0, 0,  4, 34, 94,  85;

%e   0, 0, 0, 0,  1, 18, 99, 219, 171;

%e   0, 0, 0, 0,  0,  5, 60, 261, 492,  341;

%e   0, 0, 0, 0,  0,  1, 25, 195, 678, 1101, 683;

%Y Cf. A111006.

%K easy,nonn,tabl

%O 0,6

%A _Paul Barry_, Oct 05 2005