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A103452 Inverse of number triangle A103451. 7
1, -1, 1, -1, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are 0^n. Diagonal sums are 0^n - (1-(-1)^n)/2.

Triangle T(n,k), 0<=k<=n, read by rows given by [ -1, 2, 0, 0, 0, 0, 0, ...] DELTA [1, 0, -1/2, 1/2, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938 . - Philippe Deléham, May 01 2007

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..10010 (Rows 0 <= n <= 140)

FORMULA

Number triangle T(n, k) = if(n=k, 1, if(n>0 and k=0, -1, 0))

G.f.: (1 - 2*x + y*x^2)/((1-x)*(1-y*x)). - Philippe Deléham, Feb 11 2012

EXAMPLE

Rows start {1}, {-1,1}, {-1,0,1}, {-1,0,0,1}, {-1,0,0,0,1},....

Triangle begins

1,

-1, 1,

-1, 0, 1,

-1, 0, 0, 1,

-1, 0, 0, 0, 1,

-1, 0, 0, 0, 0, 1,

-1, 0, 0, 0, 0, 0, 1,

-1, 0, 0, 0, 0, 0, 0, 1,

-1, 0, 0, 0, 0, 0, 0, 0, 1,

-1, 0, 0, 0, 0, 0, 0, 0, 0, 1,

-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Production matrix begins

-1, 1,

-2, 1, 1,

-2, 1, 0, 1,

-2, 1, 0, 0, 1,

-2, 1, 0, 0, 0, 1,

-2, 1, 0, 0, 0, 0, 1,

-2, 1, 0, 0, 0, 0, 0, 1,

-2, 1, 0, 0, 0, 0, 0, 0, 1

MATHEMATICA

Table[Range[n] /. {k_ /; k == 1 && n != 1 -> -1, k_ /; k == n -> 1, _Integer -> 0}, {n, 15}] // Flatten (* Michael De Vlieger, Jul 21 2016 *)

CROSSREFS

Cf. A103453, A103454, A103455

Sequence in context: A270885 A127972 A103451 * A131219 A127970 A158856

Adjacent sequences:  A103449 A103450 A103451 * A103453 A103454 A103455

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Feb 06 2005

STATUS

approved

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Last modified November 13 10:50 EST 2019. Contains 329093 sequences. (Running on oeis4.)