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A304223
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Triangle read by rows: T(0,0)=1; T(n,k) = T(n-1,k)-2*T(n-2,k-1)+2*T(n-3,k-2) for k = 0..floor(2*n/3); T(n,k)=0 for n or k < 0.
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1
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1, 1, 1, -2, 1, -4, 2, 1, -6, 8, 1, -8, 18, -8, 1, -10, 32, -32, 4, 1, -12, 50, -80, 36, 1, -14, 72, -160, 136, -24, 1, -16, 98, -280, 360, -160, 8, 1, -18, 128, -448, 780, -592, 128, 1, -20, 162, -672, 1484, -1632, 720, -64
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OFFSET
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0,4
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COMMENTS
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The numbers in rows of the triangle are along skew diagonals pointing top-left in center-justified triangle given in A304209.
The coefficients in the expansion of 1/(1-x+2*x^2-2*x^3) are given by the sequence generated by the row sums.
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REFERENCES
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Shara Lalo and Zagros Lalo, Polynomial Expansion Theorems and Number Triangles, Zana Publishing, 2018, ISBN: 978-1-9995914-0-3, pp. 204, 205.
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LINKS
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EXAMPLE
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Triangle begins:
1;
1;
1, -2;
1, -4, 2;
1, -6, 8;
1, -8, 18, -8;
1, -10, 32, -32, 4;
1, -12, 50, -80, 36;
1, -14, 72, -160, 136, -24;
1, -16, 98, -280, 360, -160, 8;
1, -18, 128, -448, 780, -592, 128;
1, -20, 162, -672, 1484, -1632, 720, -64;
1, -22, 200, -960, 2576, -3752, 2624, -640, 16;
...
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PROG
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(PARI) T(n, k) = if ((n<0) || (k<0), 0, if ((n==0) && (k==0), 1, T(n-1, k)-2*T(n-2, k-1)+2*T(n-3, k-2)));
tabf(nn) = for (n=0, nn, for (k=0, 2*n\3, print1(T(n, k), ", ")); print); \\ Michel Marcus, May 10 2018
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CROSSREFS
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KEYWORD
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tabf,easy,sign
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AUTHOR
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STATUS
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approved
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