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A108561
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Triangle read by rows: T(n,0)=1, T(n,n)=(-1)^floor(n/2), T(n+1,k)=T(n,k-1)+T(n,k) for 0<k<n.
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15
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1, 1, -1, 1, 0, 1, 1, 1, 1, -1, 1, 2, 2, 0, 1, 1, 3, 4, 2, 1, -1, 1, 4, 7, 6, 3, 0, 1, 1, 5, 11, 13, 9, 3, 1, -1, 1, 6, 16, 24, 22, 12, 4, 0, 1, 1, 7, 22, 40, 46, 34, 16, 4, 1, -1, 1, 8, 29, 62, 86, 80, 50, 20, 5, 0, 1, 1, 9, 37, 91, 148, 166, 130, 70, 25, 5, 1, -1, 1, 10, 46, 128, 239, 314, 296, 200, 95, 30, 6, 0, 1, 1, 11, 56, 174, 367
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refs;
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internal format)
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OFFSET
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0,12
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COMMENTS
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Sum(T(n,k): 0<=k<=n) = A078008(n);
Sum(abs(T(n,k)): 0<=k<=n) = A052953(n-1) for n>0;
T(n,1) = n - 2 for n>1;
T(n,2) = A000124(n-3) for n>2;
T(n,3) = A003600(n-4) for n>4;
T(n,n-6) = A001753(n-6) for n>6;
T(n,n-5) = A001752(n-5) for n>5;
T(n,n-4) = A002623(n-4) for n>4;
T(n,n-3) = A002620(n-1) for n>3;
T(n,n-2) = A008619(n-2) for n>2;
T(n,n-1) = n mod 2 for n>0;
T(2*n,n) = A072547(n+1).
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LINKS
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Table of n, a(n) for n=0..95.
Index entries for triangles and arrays related to Pascal's triangle
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MATHEMATICA
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Clear[t]; t[n_, 0] = 1; t[n_, n_] := t[n, n] = (-1)^Mod[n, 2]; t[n_, k_] := t[n, k] = t[n-1, k] + t[n-1, k-1]; Table[t[n, k], {n, 0, 13}, {k, 0, n}] // Flatten (* Jean-François Alcover, Mar 06 2013 *)
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CROSSREFS
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Cf. A007318.
Similar to the triangles A035317, A059259, A080242, A112555.
Sequence in context: A192062 A172371 A112555 * A174626 A104579 A079531
Adjacent sequences: A108558 A108559 A108560 * A108562 A108563 A108564
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KEYWORD
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sign,tabl
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AUTHOR
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Reinhard Zumkeller, Jun 10 2005
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STATUS
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approved
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