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A115359
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Matrix (1,x)-(x,x^2) in Riordan array notation.
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10
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1, -1, 1, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 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, 0, 0, 1
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OFFSET
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0,1
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COMMENTS
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Row sums are 1,0,1,0,1,0... Diagonal sums are A115360. Inverse is A115361.
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LINKS
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FORMULA
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Number triangle T(n, k)=if(n=k, 1, 0) OR if(n=2k+1, -1, 0).
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EXAMPLE
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Triangle begins:
1;
-1, 1;
0, 0, 1;
0, -1, 0, 1;
0, 0, 0, 0, 1;
0, 0, -1, 0, 0, 1;
0, 0, 0, 0, 0, 0, 1;
0, 0, 0, -1, 0, 0, 0, 1;
0, 0, 0, 0, 0, 0, 0, 0, 1;
0, 0, 0, 0, -1, 0, 0, 0, 0, 1;
...
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PROG
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(PARI) tabl(nn) = {T = matrix(nn, nn, n, k, n--; k--; if ((n==k), 1, if (n==2*k+1, -1, 0))); for (n=1, nn, for (k=1, n, print1(T[n, k], ", "); ); print(); ); } \\ Michel Marcus, Mar 28 2015
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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