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1, 1, 1, 1, -2, 1, 1, -2, -2, 1, 1, -11, -11, -11, 1, 1, -20, -29, -29, -20, 1, 1, -56, -74, -83, -74, -56, 1, 1, -119, -173, -191, -191, -173, -119, 1, 1, -290, -407, -461, -470, -461, -407, -290, 1, 1, -650, -938, -1055, -1100, -1100, -1055, -938, -650, 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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COMMENTS
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Row sums are s(n) = {1, 2, 0, -2, -31, -96, -341, -964, -2784, -7484, -20041, ...}, obey s(n) = 3*s(n-1) + 3*s(n-2) - 11*s(n-3) - 3*s(n-4) + 9*s(n-5) and have g.f. (1-x+3*x^3-9*x^2)/((1-x)*(1-x-3*x^2)^2).
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LINKS
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FORMULA
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T(n,k) = T(n,n-k).
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, -2, 1;
1, -2, -2, 1;
1, -11, -11, -11, 1;
1, -20, -29, -29, -20, 1;
1, -56, -74, -83, -74, -56, 1;
1, -119, -173, -191, -191, -173, -119, 1;
1, -290, -407, -461, -470, -461, -407, -290, 1;
1, -650, -938, -1055, -1100, -1100, -1055, -938, -650, 1;
1, -1523, -2171, -2459, -2567, -2603, -2567, -2459, -2171, -1523, 1;
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MAPLE
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MATHEMATICA
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A006130[n_]:= Sum[Binomial[n-j, j]*3^j, {j, 0, n}]; T[n_, k_]:= A006130[k] - A006130[n] + A006130[n-k]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Nov 24 2019 *)
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PROG
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(PARI) A006130(n) = sum(j=0, n, binomial(n-j, j)*3^j);
(Magma) A006130:= func< n | &+[Binomial(n-j, j)*3^j: j in [0..n]] >;
(Sage)
def A006130(n): return sum(binomial(n-j, j)*3^j for j in (0..n))
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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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