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A110427
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The r-th term of the n-th row of the following array contains the sum of r successively decreasing integers beginning from n. 0 < r <= n. Sequence contains the leading diagonal.
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5
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1, 1, -3, -14, -35, -69, -119, -188, -279, -395, -539, -714, -923, -1169, -1455, -1784, -2159, -2583, -3059, -3590, -4179, -4829, -5543, -6324, -7175, -8099, -9099, -10178, -11339, -12585, -13919, -15344, -16863, -18479, -20195, -22014, -23939, -25973, -28119, -30380, -32759, -35259, -37883
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = n*(1 + 2*n - n^2)/2 = n - A002411(n-1).
G.f.: x*(1 - 3*x - x^2)/(1-x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
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EXAMPLE
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E.g., the row corresponding to 4 contains 4, (3+2),{(1) +(0)+(-1)}, {(-2)+(-3)+(-4)+(-5)} ----> 4,5,0,-14
1
2 1
3 3 -3
4 5 0 -14
5 7 3 -10 -35
6 9 6 -6 -30 -69
...
Sequence contains the leading diagonal.
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PROG
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(PLT DrScheme)
;; see A110425 for definition of that function.
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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