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 A124080 10 times triangular numbers: a(n) = 5*n*(n + 1). 14
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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 LINKS Ivan Panchenko, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3, -3, 1). FORMULA a(n) = 10*C(n,2), n >= 1. a(n) = A049598(n) - A002378(n). - Zerinvary Lajos, Mar 06 2007 a(n) = 5*n*(n + 1), n >= 0. - Zerinvary Lajos, Mar 06 2007 a(n) = 5*n^2 + 5*n = 10*A000217(n) = 5*A002378(n) = 2*A028895(n). - Omar E. Pol, Dec 12 2008 a(n) = 10*n + a(n-1) (with a(0) = 0). - Vincenzo Librandi, Nov 12 2009 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 a(n) = A062786(n+1) - 1. - Omar E. Pol, Oct 03 2011 a(n) = A131242(10*n+9). - Philippe Deléham, Mar 27 2013 From G. C. Greubel, Aug 22 2017: (Start) G.f.: 10*x/(1 - x)^3. E.g.f.: 5*x*(x + 2)*exp(x). (End) MAPLE [seq(10*binomial(n, 2), n=1..51)]; seq(n*(n+1)*5, n=0..39); # Zerinvary Lajos, Mar 06 2007 MATHEMATICA 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 (PARI) a(n)=5*n*(n+1) \\ Charles R Greathouse IV, Sep 28 2015 CROSSREFS Cf. A028895, A046092, A045943, A002378, A028896, A024966, A033996, A027468, A049598, A000217. Sequence in context: A318624 A255601 A104044 * A034127 A229466 A269261 Adjacent sequences:  A124077 A124078 A124079 * A124081 A124082 A124083 KEYWORD easy,nonn AUTHOR Zerinvary Lajos, Nov 24 2006 STATUS approved

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Last modified May 8 19:28 EDT 2021. Contains 343666 sequences. (Running on oeis4.)