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.
%I A249999 #23 Feb 11 2025 13:59:57
%S A249999 1,7,32,122,423,1389,4414,13744,42245,128771,390396,1179366,3554467,
%T A249999 10696153,32153978,96592988,290041089,870647535,2612991160,7841070610,
%U A249999 23527406111,70590606917,211788597942,635399348232,1906265153533,5718929678299,17157057470324,51471709281854
%N A249999 Expansion of 1/((1-x)^2*(1-2*x)*(1-3*x)).
%H A249999 G. C. Greubel, <a href="/A249999/b249999.txt">Table of n, a(n) for n = 0..1000</a>
%H A249999 Anthony G. Shannon, Hakan Akkuş, Yeşim Aküzüm, Ömür Deveci, and Engin Özkan, <a href="https://doi.org/10.7546/nntdm.2024.30.3.530-537">A partial recurrence Fibonacci link</a>, Notes Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 530-537. See Table 2, p. 534.
%H A249999 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-17,17,-6).
%F A249999 G.f.: 1/((1-x)^2 * (1-2*x) * (1-3*x)).
%F A249999 a(n) = 9/4 - 2^(n+3) + n/2 + 3^(n+3)/4. - _R. J. Mathar_, Jan 09 2015
%F A249999 E.g.f.: (1/4)*((9 + 2*x) - 32*exp(x) + 27*exp(2*x))*exp(x). - _G. C. Greubel_, Jul 21 2022
%t A249999 LinearRecurrence[{7,-17,17,-6}, {1,7,32,122}, 50] (* _G. C. Greubel_, Jul 21 2022 *)
%t A249999 CoefficientList[Series[1/((1-x)^2(1-2x)(1-3x)),{x,0,30}],x] (* _Harvey P. Dale_, Feb 11 2025 *)
%o A249999 (Magma) [(2*n +9 -2^(n+5) +3^(n+3))/4: n in [0..50]]; // _G. C. Greubel_, Jul 21 2022
%o A249999 (SageMath) [(2*n+9 -2^(n+5) +3^(n+3))/4 for n in (0..50)] # _G. C. Greubel_, Jul 21 2022
%Y A249999 Cf. A000392 (first differences), A094705, A243869, A249997.
%K A249999 nonn,easy
%O A249999 0,2
%A A249999 _Alex Ratushnyak_, Dec 28 2014