

A124080


10 times triangular numbers: 5n(n+1).


11



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

0,2


COMMENTS

If Y is a 5subset of an nset X then, for n>=5, a(n4) is equal to the number of 5subsets of X having exactly three elements in common with Y. Y is a 5subset of an nset X then, for n>=6, a(n6) is the number of (n5)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


LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000


FORMULA

a(n) = 10*C(n,2), n>=1.
a(n) = A049598(n)  A002378(n).  Zerinvary Lajos, Mar 06 2007
a(n) = n*(n+1)*5, n>=0.  Zerinvary Lajos, Mar 06 2007
a(n) = 5n^2 + 5n = A000217(n)*10 = A002378(n)*5 = A028895(n)*2.  Omar E. Pol, Dec 12 2008
a(n) = 10*n+a(n1) (with a(0)=0).  Vincenzo Librandi, Nov 12 2009
a(n) = 3*a(n1)3*a(n2)+a(n3), a(0)=0, a(1)=10, a(2)=30.  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


MAPLE

[seq(10*binomial(n, 2), n=1..51)];
seq(n*(n+1)*5, n=0..39); # Zerinvary Lajos, Mar 06 2007


MATHEMATICA

s=0; lst={s}; Do[s+=n++ +10; AppendTo[lst, s], {n, 0, 8!, 10}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 17 2008 *)
10*Accumulate[Range[0, 50]] (* or *) LinearRecurrence[{3, 3, 1}, {0, 10, 30}, 50](* Harvey P. Dale, Jul 21 2011 *)


PROG

(MAGMA) [ 5*n*(n+1) : n in [0..50] ]; // Wesley Ivan Hurt, Jun 09 2014


CROSSREFS

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 A229466 A005052
Adjacent sequences: A124077 A124078 A124079 * A124081 A124082 A124083


KEYWORD

easy,nonn


AUTHOR

Zerinvary Lajos, Nov 24 2006


STATUS

approved



