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A124080
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10 times triangular numbers: a(n) = 5*n*(n + 1).
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15
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0, 10, 30, 60, 100, 150, 210, 280, 360, 450, 550, 660, 780, 910, 1050, 1200, 1360, 1530, 1710, 1900, 2100, 2310, 2530, 2760, 3000, 3250, 3510, 3780, 4060, 4350, 4650, 4960, 5280, 5610, 5950, 6300, 6660, 7030, 7410, 7800, 8200, 8610, 9030, 9460, 9900, 10350
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OFFSET
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0,2
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COMMENTS
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If Y is a 5-subset of an n-set X then, for n >= 5, a(n-4) is equal to the number of 5-subsets of X having exactly three elements in common with Y. Y is a 5-subset of an n-set X then, for n >= 6, a(n-6) is the number of (n-5)-subsets of X having exactly two elements in common with Y. - Milan Janjic, Dec 28 2007
Also sequence found by reading the line from 0, in the direction 0, 10, ... and the same line from 0, in the direction 0, 30, ..., in the square spiral whose vertices are the generalized dodecagonal numbers A195162. Axis perpendicular to A195148 in the same spiral. - Omar E. Pol, Sep 18 2011
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LINKS
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FORMULA
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a(n) = 10*C(n,2), n >= 1.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), a(0) = 0, a(1) = 10, a(2) = 30. - Harvey P. Dale, Jul 21 2011
G.f.: 10*x/(1 - x)^3.
E.g.f.: 5*x*(x + 2)*exp(x). (End)
Sum_{n>=1} 1/a(n) = 1/5.
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2)-1)/5. (End)
Product_{n>=1} (1 - 1/a(n)) = -(5/Pi)*cos(3*Pi/(2*sqrt(5))).
Product_{n>=1} (1 + 1/a(n)) = (5/Pi)*cos(Pi/(2*sqrt(5))). (End)
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MAPLE
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[seq(10*binomial(n, 2), n=1..51)];
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MATHEMATICA
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10*Accumulate[Range[0, 50]] (* or *) LinearRecurrence[{3, -3, 1}, {0, 10, 30}, 50] (* Harvey P. Dale, Jul 21 2011 *)
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PROG
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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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