A115450 Number triangle (1/((1-x)(1-2x)),-x)-(x/((1-x)(1-2x)),-x^2) (expressed in the notation of Riordan arrays).

1, 2, -1, 4, -3, 1, 8, -6, 3, -1, 16, -12, 7, -3, 1, 32, -24, 14, -7, 3, -1, 64, -48, 28, -15, 7, -3, 1, 128, -96, 56, -30, 15, -7, 3, -1, 256, -192, 112, -60, 31, -15, 7, -3, 1, 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

Offset: 0

Author

Paul Barry, Jan 22 2006

Keywords

• easy
• sign
• tabl

Comments

Row sums are A115451. Inverse is A115452. Row sums of inverse matrix are the Fredholm-Rueppel sequence A036987.

Examples

			Triangle begins
1,
2, -1,
4, -3, 1,
8, -6, 3, -1,
16, -12, 7, -3, 1,
32, -24, 14, -7, 3, -1,
64, -48, 28, -15, 7, -3, 1,
128, -96, 56, -30, 15, -7, 3, -1,
256, -192, 112, -60, 31, -15, 7, -3, 1,
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, -1,
4096, -3072, 1792, -960, 496, -252, 127, -63, 31, -15, 7, -3, 1
		

Formula

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.