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 A033994 a(n) = n*(n+1)*(5*n+1)/6. 16
 2, 11, 32, 70, 130, 217, 336, 492, 690, 935, 1232, 1586, 2002, 2485, 3040, 3672, 4386, 5187, 6080, 7070, 8162, 9361, 10672, 12100, 13650, 15327, 17136, 19082, 21170, 23405, 25792, 28336, 31042, 33915, 36960, 40182, 43586, 47177, 50960, 54940 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Partial sums of A005476. a(n) is the dot product of the vectors of the first n positive integers and the next n integers. - Michel Marcus, Sep 02 2020 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA G.f.: x*(2+3*x)/(1-x)^4. a(n) = A132121(n,1). - Reinhard Zumkeller, Aug 12 2007 a(n) = A000292(n) + A002412(n) = A000330(n) + A002411(n). - Omar E. Pol, Jan 11 2013 a(n) = Sum_{i=1..n} Sum_{j=1..n} i+min(i,j). - Enrique Pérez Herrero, Jan 15 2013 a(n) = Sum_{i=1..n} i*(n+i). - Charlie Marion, Apr 10 2013 Sum_{n>=1} 1/a(n) = 36 - 3*Pi*5^(3/4)*phi^(3/2)/4 - 15*sqrt(5)*log(phi)/4 - 75*log(5)/8 = 0.66131826232008423794478..., where phi = A001622 = (1 + sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jun 01 2018 MAPLE [n*(n+1)*(5*n+1)/6\$n=1..40]; # Muniru A Asiru, Jan 01 2019 MATHEMATICA Table[Range[x].Range[x+1, 2x], {x, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {2, 11, 32, 70}, 40] (* Harvey P. Dale, Jun 01 2018 *) PROG (PARI) a(n) = n*(n+1)*(5*n+1)/6; (MAGMA) [n*(n+1)*(5*n+1)/6 : n in [1..40]]; // Vincenzo Librandi, Jan 01 2019 (GAP) a:=List([1..40], n->n*(n+1)*(5*n+1)/6);; Print(a); # Muniru A Asiru, Jan 01 2019 CROSSREFS Cf. A005476, A016873, A000330, A132124, A132112, A050409. Sequence in context: A190261 A000755 A183460 * A023659 A094792 A173707 Adjacent sequences:  A033991 A033992 A033993 * A033995 A033996 A033997 KEYWORD easy,nonn AUTHOR Barry E. Williams, Dec 16 1999 EXTENSIONS More terms from James A. Sellers, Jan 19 2000 STATUS approved

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Last modified January 27 19:46 EST 2021. Contains 340479 sequences. (Running on oeis4.)