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A092286
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Fourth diagonal (m=3) of triangle A084938; a(n) = A084938(n+3,n) = (n^3 + 9*n^2 + 26*n)/6.
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2
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0, 6, 16, 31, 52, 80, 116, 161, 216, 282, 360, 451, 556, 676, 812, 965, 1136, 1326, 1536, 1767, 2020, 2296, 2596, 2921, 3272, 3650, 4056, 4491, 4956, 5452, 5980, 6541, 7136, 7766, 8432, 9135, 9876, 10656, 11476, 12337, 13240, 14186, 15176
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OFFSET
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0,2
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COMMENTS
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If X is an n-set and Y a fixed (n-4)-subset of X then a(n-4) is equal to the number of 3-subsets of X intersecting Y. - Milan Janjic, Aug 15 2007
For n>=0, A092286(n) is the number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = n + 1. A092286(n) is also the number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = 3n - 1. - Clark Kimberling, Mar 20 2012
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LINKS
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FORMULA
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a(n) = 1/2 * sum_{k=1..n} (k+3)(k+2).
a(n) = 1/6 * n *(n^2 + 9n + 26). (End)
G.f.: x*(6 - 8*x + 3*x^2)/(1-x)^4. - Colin Barker, Mar 18 2012
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MAPLE
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a:=n->(n^3 + 9*n^2 + 26*n)/6: seq(a(n), n=3..45);
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MATHEMATICA
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Table[(n^3 + 9*n^2 + 26*n)/6, {n, 0, 100}] (* T. D. Noe, Apr 12 2011 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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