Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #23 Oct 27 2024 18:58:54
%S 6,33,80,147,234,341,468,615,782,969,1176,1403,1650,1917,2204,2511,
%T 2838,3185,3552,3939,4346,4773,5220,5687,6174,6681,7208,7755,8322,
%U 8909,9516,10143,10790,11457,12144,12851,13578,14325,15092,15879,16686,17513
%N a(n) = (2*n + 1)*(5*n + 6).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = A153126(2*n+1) = A000566(2*(n+1)) - 1.
%F a(n) = a(n-1) + 20*n + 7 (with a(0)=6). - _Vincenzo Librandi_, Dec 27 2010
%F G.f.: (-6-15*x+x^2)/(-1+x)^3 - _Harvey P. Dale_, Jun 07 2021
%F Sum_{n>=0} 1/a(n) = 5/7 - sqrt(1+2/sqrt(5))*Pi/14 - sqrt(5)*log(phi)/14 - 5*log(5)/28 + 2*log(2)/7, where phi is the golden ratio (A001622). - _Amiram Eldar_, Aug 23 2022
%F From _Elmo R. Oliveira_, Oct 27 2024: (Start)
%F E.g.f.: exp(x)*(6 + 27*x + 10*x^2).
%F a(n) = A005408(n)*A016861(n+1).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t Table[(2n+1)(5n+6),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{6,33,80},50] (* _Harvey P. Dale_, Jun 07 2021 *)
%o (PARI) a(n)=(2*n+1)*(5*n+6) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A000566, A001622, A005408, A016861, A019952, A033571, A153126.
%K nonn,easy
%O 0,1
%A _Reinhard Zumkeller_, Dec 20 2008