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A124080
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10 times triangular numbers.
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10
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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.lso, if - 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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Table of n, a(n) for n=0..45.
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FORMULA
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a(n)=10*C(n,2), n>=1
a(n)=A049598-A002378. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 06 2007
a(n)=n*(n+1)*5, n>=0 . - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 06 2007
a(n) = 5n^2 + 5n = A000217(n)*10 = A002378(n)*5 = A028895(n)*2. [From Omar E. Pol, Dec 12 2008]
a(n)=10*n+a(n-1) (with a(0)=0) [From Vincenzo Librandi
a(0)=0, a(1)=10, a(2)=30, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, Jul 21 2011]
a(n) = A062786(n+1) - 1. - Omar E. Pol, Oct 03 2011
a(n) = A131242(10n+9). - Philippe Deléham, Mar 27 2013
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MAPLE
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[seq(10*binomial(n, 2), n=1..51)];
seq(n*(n+1)*5, n=0..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 06 2007
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +10; AppendTo[lst, s], {n, 0, 8!, 10}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 17 2008]
10*Accumulate[Range[0, 50]] (* or *) LinearRecurrence[{3, -3, 1}, {0, 10, 30}, 50](* From Harvey P. Dale, Jul 21 2011 *)
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CROSSREFS
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Cf. A028895, A046092, A045943, A002378, A028896, A024966, A033996, A027468.
Cf. A002378, A049598.
Cf. A000217. [From Omar E. Pol, Dec 12 2008]
Sequence in context: A031299 A124164 A104044 * A034127 A005052 A057344
Adjacent sequences: A124077 A124078 A124079 * A124081 A124082 A124083
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KEYWORD
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easy,nonn
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AUTHOR
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Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 24 2006
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STATUS
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approved
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