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 A303302 #37 Dec 02 2024 18:12:34
%S A303302 0,34,136,306,544,850,1224,1666,2176,2754,3400,4114,4896,5746,6664,
%T A303302 7650,8704,9826,11016,12274,13600,14994,16456,17986,19584,21250,22984,
%U A303302 24786,26656,28594,30600,32674,34816,37026,39304,41650,44064,46546,49096,51714,54400,57154,59976,62866,65824,68850,71944
%N A303302 a(n) = 34*n^2.
%C A303302 Sequence found by reading the line from 0, in the direction 0, 34, ..., in the square spiral whose vertices are the generalized 19-gonal numbers A303813.
%H A303302 Colin Barker, <a href="/A303302/b303302.txt">Table of n, a(n) for n = 0..1000</a>
%H A303302 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A303302 a(n) = 34*A000290(n) = 17*A001105(n) = 2*A244630(n).
%F A303302 G.f.: 34*x*(1 + x)/(1 - x)^3. - _Vincenzo Librandi_, Jun 07 2018
%F A303302 From _Elmo R. Oliveira_, Dec 02 2024: (Start)
%F A303302 E.g.f.: 34*x*(1 + x)*exp(x).
%F A303302 a(n) = A005843(n)*A008599(n).
%F A303302 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A303302 Table[34 n^2, {n, 0, 40}]
%t A303302 LinearRecurrence[{3,-3,1},{0,34,136},50] (* _Harvey P. Dale_, Jul 23 2018 *)
%o A303302 (PARI) a(n) = 34*n^2;
%o A303302 (PARI) concat(0, Vec(34*x*(1 + x) / (1 - x)^3 + O(x^40))) \\ _Colin Barker_, Jun 12 2018
%o A303302 (Magma) [34*n^2: n in [0..50]]; // _Vincenzo Librandi_ Jun 07 2018
%Y A303302 Cf. A005843, A008599, A303813.
%Y A303302 Cf. similar sequences of the type k*n^2: A000290 (k=1), A001105 (k=2), A033428 (k=3), A016742 (k=4), A033429 (k=5), A033581 (k=6), A033582 (k=7), A139098 (k=8), A016766 (k=9), A033583 (k=10), A033584 (k=11), A135453 (k=12), A152742 (k=13), A144555 (k=14), A064761 (k=15), A016802 (k=16), A244630 (k=17), A195321 (k=18), A244631 (k=19), A195322 (k=20), A064762 (k=21), A195323 (k=22), A244632 (k=23), A195824 (k=24), A016850 (k=25), A244633 (k=26), A244634 (k=27), A064763 (k=28), A244635 (k=29), A244636 (k=30), A244082 (k=32), this sequence (k=34), A016910 (k=36), A016982 (k=49), A017066 (k=64), A017162 (k=81), A017270 (k=100), A017390 (k=121), A017522 (k=144).
%K A303302 nonn,easy
%O A303302 0,2
%A A303302 _Omar E. Pol_, May 13 2018