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A055795
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a(n) = binomial(n,4) + binomial(n,2).
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17
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0, 1, 3, 7, 15, 30, 56, 98, 162, 255, 385, 561, 793, 1092, 1470, 1940, 2516, 3213, 4047, 5035, 6195, 7546, 9108, 10902, 12950, 15275, 17901, 20853, 24157, 27840, 31930, 36456, 41448, 46937, 52955, 59535, 66711, 74518, 82992, 92170, 102090, 112791, 124313, 136697
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OFFSET
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1,3
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COMMENTS
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Answer to the question: if you have a tall building and 4 plates and you need to find the highest story from which a plate thrown does not break, what is the number of stories you can handle given n tries?
If Y is a 2-subset of an n-set X then, for n >= 4, a(n-3) is the number of 4-subsets of X which do not have exactly one element in common with Y. - Milan Janjic, Dec 28 2007
Also the number of maximal cliques in the n-tetrahedral graph for n > 5. - Eric W. Weisstein, Jun 12 2017
Mark each point on an 8^(n-2) grid with the number of points that are visible from the point; for n > 3, a(n) is the number of distinct values in the grid. - Torlach Rush, Mar 25 2021
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LINKS
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FORMULA
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a(1) = 1; a(n) = a(n-1) + 1 + A004006(n-1).
Row sums of triangle A134394. Also, binomial transform of [1, 2, 2, 2, 1, 0, 0, 0, ...]. - Gary W. Adamson, Oct 23 2007
a(n) = n*(n^3 - 6*n^2 + 23*n - 18)/24. - Gary Detlefs, Dec 08 2011
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5); a(1)=0, a(2)=1, a(3)=3, a(4)=7, a(5)=15. - Harvey P. Dale, Dec 07 2015
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MAPLE
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MATHEMATICA
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Table[n (n^3 - 6 n^2 + 23 n - 18)/24, {n, 100}] (* Wesley Ivan Hurt, Sep 29 2013 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 3, 7, 15}, 50] (* Harvey P. Dale, Dec 07 2015 *)
CoefficientList[Series[x (-1 + 2 x - 2 x^2)/(-1 + x)^5, {x, 0, 20}], x] (* Eric W. Weisstein, Dec 01 2017~ *)
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PROG
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(Magma) [n*(n^3-6*n^2+23*n-18)/24: n in [1..100]]; // Wesley Ivan Hurt, Sep 29 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Offset corrected and Sellers formula adjusted by Gary Detlefs, Nov 28 2011
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STATUS
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approved
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