cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A027965 T(n, 2*n-3), T given by A027960.

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%I A027965 #13 Oct 18 2022 15:01:41
%S A027965 3,7,15,28,47,73,107,150,203,267,343,432,535,653,787,938,1107,1295,
%T A027965 1503,1732,1983,2257,2555,2878,3227,3603,4007,4440,4903,5397,5923,
%U A027965 6482,7075,7703,8367,9068,9807,10585,11403,12262,13163,14107,15095,16128,17207,18333,19507,20730,22003
%N A027965 T(n, 2*n-3), T given by A027960.
%H A027965 G. C. Greubel, <a href="/A027965/b027965.txt">Table of n, a(n) for n = 2..1000</a>
%H A027965 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A027965 a(n+2) = A074742(n-1) = A008778(n) + 2 = A000297(n-1) + 3.
%F A027965 From _Ralf Stephan_, Feb 07 2004: (Start)
%F A027965 G.f.: x^2*(3 - 2*x)*(1 - x + x^2)/(1-x)^4.
%F A027965 Differences of A027966. (End)
%F A027965 From _G. C. Greubel_, Jun 30 2019: (Start)
%F A027965 a(n) = (18 - 10*n + 3*n^2 + n^3)/6.
%F A027965 E.g.f.: (-18 - 12*x + (18 - 6*x + 6*x^2 + x^3)*exp(x))/6. (End)
%t A027965 LinearRecurrence[{4,-6,4,-1}, {3,7,15,28}, 50] (* _G. C. Greubel_, Jun 30 2019 *)
%o A027965 (PARI) vector(50, n, n++; (18-10*n+3*n^2+n^3)/6) \\ _G. C. Greubel_, Jun 30 2019
%o A027965 (Magma) [(18-10*n+3*n^2+n^3)/6: n in [2..50]]; // _G. C. Greubel_, Jun 30 2019
%o A027965 (Sage) [(18-10*n+3*n^2+n^3)/6 for n in (2..50)] # _G. C. Greubel_, Jun 30 2019
%o A027965 (GAP) List([2..50], n-> (18-10*n+3*n^2+n^3)/6) # _G. C. Greubel_, Jun 30 2019
%Y A027965 A column of triangle A027011.
%K A027965 nonn,easy
%O A027965 2,1
%A A027965 _Clark Kimberling_
%E A027965 Terms a(32) onward added by _G. C. Greubel_, Jun 30 2019