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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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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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 R. Janjic (agnus(AT)blic.net), Aug 15 2007
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LINKS
| Milan Janjic, Two Enumerative Functions
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FORMULA
| a(n) = A084938(n+3, n) = Sum_{k=0..3} A090238(3, k)*binomial(n, k).
a(n+ 1/2 * sum ((k+3)!/(k+1)!,k=12..,n) a(n)= 1/6 * n *(n^2+9n+26) [From Gary Detlefs (gdetlefs(AT)aol.com), Aug 02 2010]
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MAPLE
| a:=n->(n^3 + 9*n^2 + 26*n)/6: seq(a(n), n=3..45);
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MATHEMATICA
| q=60; (Transpose[NestList[Accumulate, Range[q], q]]-Range[q])[[4]] (*From Vladimir Joseph Stephan Orlovsky, Apr 8 2011*)
Table[(n^3 + 9*n^2 + 26*n)/6, {n, 0, 100}] (* T. D. Noe, Apr 12 2011 *)
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CROSSREFS
| Cf. A084938 A090238.
Sequence in context: A102214 A115007 A005891 * A108182 A097118 A134465
Adjacent sequences: A092283 A092284 A092285 * A092287 A092288 A092289
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KEYWORD
| easy,nonn
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AUTHOR
| DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 30 2004
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