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A172090
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Triangle T(n, k) = f(n-k) + f(k) - f(n), where f(n) = -3*n with f(0) = 1, f(1) = -2, read by rows.
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1
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1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n, k) = f(n-k) + f(k) - f(n), where f(n) = -3*n with f(0) = 1, f(1) = -2.
T(n, k) is defined by T(n, 0) = T(n, 1) = T(n, n-1) = T(n, n) = T(3, k) = 1, T(2, 1) = 2 and 0 otherwise.
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, 2, 1;
1, 1, 1, 1;
1, 1, 0, 1, 1;
1, 1, 0, 0, 1, 1;
1, 1, 0, 0, 0, 1, 1;
1, 1, 0, 0, 0, 0, 1, 1;
1, 1, 0, 0, 0, 0, 0, 1, 1;
1, 1, 0, 0, 0, 0, 0, 0, 1, 1;
1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1;
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MATHEMATICA
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(* First program *)
f[n_]:= f[n]= If[n < 2, (-1)^n*(n+1), -3*n];
T[n_, k_]:= f[n-k] +f[k] -f[n];
Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Apr 29 2021 *)
(* Second program *)
T[n_, k_]:= If[n<3, Binomial[n, k], If[n==3 || k<2 || k>n-2, 1, 0]];
Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Apr 29 2021 *)
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PROG
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(Sage)
def f(n): return (-1)^n*(n+1) if (n<2) else -3*n
def T(n, k): return f(n-k) + f(k) - f(n)
flatten([[T(n, k) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Apr 29 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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