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A115952 Expansion of (1-x+x*y)/(1-x^2*y^2) - x^2/(1-x^2*y). 4
1, -1, 1, -1, 0, 1, 0, 0, -1, 1, 0, -1, 0, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are A000007. Diagonal sums are A115953. Inverse is A115954.

LINKS

G. C. Greubel, Rows n = 0..100 of triangle, flattened

FORMULA

Number triangle T(n,k)=if(n=k,1,0) OR if(n=2k+2,-1,0) OR if(n=k+1,-(1+(-1)^k)/2,0).

EXAMPLE

Triangle begins

   1,

  -1,  1,

  -1,  0,  1,

   0,  0, -1,  1,

   0, -1,  0,  0,  1,

   0,  0,  0,  0, -1,  1,

   0,  0, -1,  0,  0,  0,  1,

   0,  0,  0,  0,  0,  0, -1,  1,

   0,  0,  0, -1,  0,  0,  0,  0,  1,

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

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

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

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

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

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

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

MATHEMATICA

T[n_, k_]:= If[n==k, 1, If[n==k+1, -(1+(-1)^k)/2, If[n==2*k+2, -1, 0]]];

Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, May 06 2019 *)

PROG

(PARI) {T(n, k) = if(n==k, 1, if(n==k+1, -(1+(-1)^k)/2, if(n==2*k+2, -1, 0)))}; \\ G. C. Greubel, May 06 2019

(MAGMA) [[n eq k select 1 else n eq k+1 select -(1+(-1)^k)/2 else n eq 2*(k+1) select -1 else 0: k in [0..n]]: n in [0..15]]; // G. C. Greubel, May 06 2019

(Sage)

def T(n, k):

    if (n==k): return 1

    elif (n==k+1): return -(1+(-1)^k)/2

    elif (n==2*(k+1)): return -1

    else: return 0

[[T(n, k) for k in (0..n)] for n in (0..15)] # G. C. Greubel, May 06 2019

CROSSREFS

Cf. A115524.

Sequence in context: A283437 A155898 A181650 * A115524 A117198 A271047

Adjacent sequences:  A115949 A115950 A115951 * A115953 A115954 A115955

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Feb 02 2006

STATUS

approved

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Last modified October 26 14:28 EDT 2021. Contains 348267 sequences. (Running on oeis4.)