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A055461
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Square decrescendo subsequences: triangle T(n,k) = (n-k)^2, n >= 1, 0 <= k < n.
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6
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1, 4, 1, 9, 4, 1, 16, 9, 4, 1, 25, 16, 9, 4, 1, 36, 25, 16, 9, 4, 1, 49, 36, 25, 16, 9, 4, 1, 64, 49, 36, 25, 16, 9, 4, 1, 81, 64, 49, 36, 25, 16, 9, 4, 1, 100, 81, 64, 49, 36, 25, 16, 9, 4, 1, 121, 100, 81, 64, 49, 36, 25, 16, 9, 4, 1, 144, 121, 100, 81, 64, 49, 36, 25, 16, 9, 4, 1
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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G.f. as triangle: x*(1+x)/((1-x*y)*(1-x)^3). - Robert Israel, Jan 18 2018
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EXAMPLE
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1; 4 1; 9 4 1; 16 9 4 1; etc.
Triangle begins:
1;
4, 1;
9, 4, 1;
16, 9, 4, 1;
25, 16, 9, 4, 1;
36, 25, 16, 9, 4, 1;
49, 36, 25, 16, 9, 4, 1;
64, 49, 36, 25, 16, 9, 4, 1;
81, 64, 49, 36, 25, 16, 9, 4, 1;
100, 81, 64, 49, 36, 25, 16, 9, 4, 1;
...
For n = 7 the row sum is 49 + 36 + 25 + 16 + 9 + 4 + 1 = A000330(7) = 140. The alternating row sum is 49 - 36 + 25 - 16 + 9 - 4 + 1 = A000217(7) = 28.
(End)
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MAPLE
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for n from 1 to 10 do
seq((n-k)^2, k=0..n-1)
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MATHEMATICA
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Table[Range[n, 1, -1]^2, {n, 20}]//Flatten (* Harvey P. Dale, Apr 17 2020 *)
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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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