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A132770
a(n) = n*(n + 28).
4
0, 29, 60, 93, 128, 165, 204, 245, 288, 333, 380, 429, 480, 533, 588, 645, 704, 765, 828, 893, 960, 1029, 1100, 1173, 1248, 1325, 1404, 1485, 1568, 1653, 1740, 1829, 1920, 2013, 2108, 2205, 2304, 2405, 2508, 2613, 2720, 2829, 2940, 3053, 3168, 3285, 3404, 3525
OFFSET
0,2
LINKS
FORMULA
a(n) = 2*n + a(n-1) + 27, with a(0)=0. - Vincenzo Librandi, Aug 03 2010
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(28)/28 = A001008(28)/A102928(28) = 315404588903/2248776129600, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 7751493599/321253732800. (End)
G.f.: x*(29 - 27*x)/(1-x)^3. - Harvey P. Dale, Aug 03 2021
E.g.f.: x*(29 + x)*exp(x). - G. C. Greubel, Mar 13 2022
MATHEMATICA
#(#+28)&/@Range[0, 50] (* or *) LinearRecurrence[{3, -3, 1}, {0, 29, 60}, 50] (* Harvey P. Dale, Apr 30 2018 *)
PROG
(PARI) a(n)=n*(n+28) \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [n*(n+28) for n in (0..50)] # G. C. Greubel, Mar 13 2022
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Aug 28 2007
STATUS
approved