|
%I #2 Mar 30 2012 18:59:13
%S 1,2,-1,4,-3,1,8,-6,3,-1,16,-12,7,-3,1,32,-24,14,-7,3,-1,64,-48,28,
%T -15,7,-3,1,128,-96,56,-30,15,-7,3,-1,256,-192,112,-60,31,-15,7,-3,1,
%U 512,-384,224,-120,62,-31,15,-7,3,-1,1024,-768,448,-240,124,-63,31,-15,7,-3,1,2048,-1536,896,-480,248,-126,63,-31,15,-7,3
%N Number triangle (1/((1-x)(1-2x)),-x)-(x/((1-x)(1-2x)),-x^2) (expressed in the notation of Riordan arrays).
%C Row sums are A115451. Inverse is A115452. Row sums of inverse matrix are the Fredholm-Rueppel sequence A036987.
%F Column k has g.f. 1/((1-x)(1-2x))*(-x)^k*(1-x^(k+1)); Number triangle T(n, k)=(if(k<=n, 2^(n-k+1)-1, 0)-if(k<=floor(n/2), 2^(n-2k)-1, 0))(-1)^k.
%e Triangle begins
%e 1,
%e 2, -1,
%e 4, -3, 1,
%e 8, -6, 3, -1,
%e 16, -12, 7, -3, 1,
%e 32, -24, 14, -7, 3, -1,
%e 64, -48, 28, -15, 7, -3, 1,
%e 128, -96, 56, -30, 15, -7, 3, -1,
%e 256, -192, 112, -60, 31, -15, 7, -3, 1,
%e 512, -384, 224, -120, 62, -31, 15, -7, 3, -1,
%e 1024, -768, 448, -240, 124, -63, 31, -15, 7, -3, 1,
%e 2048, -1536, 896, -480, 248, -126, 63, -31, 15, -7, 3, -1,
%e 4096, -3072, 1792, -960, 496, -252, 127, -63, 31, -15, 7, -3, 1
%K easy,sign,tabl
%O 0,2
%A _Paul Barry_, Jan 22 2006
|
