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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 February 5 18:47 EST 2023. Contains 360087 sequences. (Running on oeis4.)