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 A162148 a(n) = n*(n+1)*(5*n+7)/6. 6
 0, 4, 17, 44, 90, 160, 259, 392, 564, 780, 1045, 1364, 1742, 2184, 2695, 3280, 3944, 4692, 5529, 6460, 7490, 8624, 9867, 11224, 12700, 14300, 16029, 17892, 19894, 22040, 24335, 26784, 29392, 32164, 35105, 38220, 41514, 44992, 48659, 52520, 56580 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Partial sums of A147875. Equals the fourth right hand column of A175136 for n>=1. - Johannes W. Meijer, May 06 2011 a(n) is the number of triples (w,x,y) havingt all terms in {0,...,n} and x+y>w. - Clark Kimberling, Jun 14 2012 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1). FORMULA a(n) = A162147(n)+A000217(n). From Johannes W. Meijer, May 06 2011: (Start) G.f.: x*(4+x)/(x-1)^4 a(n) = 4*binomial(n+2,3)+binomial(n+1,3) a(n) = A091894(3,0)*binomial(n+2,3)+ A091894(3,1)*binomial(n+1,3). (End) a(n) = (n+1)*A000290(n+1) - sum(A000217(i), i=1..n+1). a(0)=0, a(1)=4, a(2)=17, a(3)=44, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, May 20 2014 MATHEMATICA f[n_]:=5*n+4; s1=s2=0; lst={}; Do[a=f[n]; s1+=a; s2+=s1; AppendTo[lst, s2], {n, 0, 6!}]; lst Table[(n(n+1)(5n+7))/6, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 4, 17, 44}, 50] (* Harvey P. Dale, May 20 2014 *) PROG (MAGMA) [n*(n+1)*(5*n+7)/6: n in [0..50]]; // Vincenzo Librandi, May 07 2011 (PARI) a(n)=n*(n+1)*(5*n+7)/6 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A033994, A002413, A016061, A006331, A002412, A162147, A175136, A190048, A190049, A254407. Related to A000292 and A091894. Sequence in context: A275815 A018973 A212575 * A166781 A147656 A095667 Adjacent sequences:  A162145 A162146 A162147 * A162149 A162150 A162151 KEYWORD nonn,easy AUTHOR Vladimir Joseph Stephan Orlovsky, Jun 25 2009 EXTENSIONS Definition rephrased by R. J. Mathar, Jun 27 2009 STATUS approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)