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A094415
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Triangle T read by rows: dot product <r,r-1,...,1> * <s+1,s+2,...,r,1,2,...,s>.
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10
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1, 4, 5, 10, 13, 13, 20, 26, 28, 26, 35, 45, 50, 50, 45, 56, 71, 80, 83, 80, 71, 84, 105, 119, 126, 126, 119, 105, 120, 148, 168, 180, 184, 180, 168, 148, 165, 201, 228, 246, 255, 255, 246, 228, 201, 220, 265, 300, 325, 340, 345, 340, 325, 300, 265, 286, 341
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OFFSET
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0,2
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LINKS
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FORMULA
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T(n, k) = n*(n^2 + 3*n*(1+k) + 2 - 3*k^2)/6 for n >= 0, 0 <= k <= n.
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EXAMPLE
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Triangle begins as:
1;
4, 5;
10, 13, 13;
20, 26, 28, 26;
35, 45, 50, 50, 45;
56, 71, 80, 83, 80, 71;
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MAPLE
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seq(seq( (n+1)*((n+2)*(n+3) + 3*k*(n-k+1))/6 , k=0..n), n=0..12); # G. C. Greubel, Oct 30 2019
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MATHEMATICA
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Table[(n+1)*((n+2)*(n+3) + 3*k*(n-k+1))/6, {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Oct 30 2019 *)
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PROG
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(PARI) T(n, k) = (n+1)*((n+2)*(n+3) + 3*k*(n-k+1))/6;
for(n=0, 12, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Oct 30 2019
(Magma) [(n+1)*((n+2)*(n+3) + 3*k*(n-k+1))/6: k in [0..n], n in [0..12]]; // G. C. Greubel, Oct 30 2019
(Sage) [[(n+1)*((n+2)*(n+3) + 3*k*(n-k+1))/6 for k in (0..n)] for n in (0..12)] # G. C. Greubel, Oct 30 2019
(GAP) Flat(List([0..12], n-> List([0..n], k-> (n+1)*((n+2)*(n+3) + 3*k*(n-k+1))/6 ))); # G. C. Greubel, Oct 30 2019
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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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