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 A303299 #36 Mar 01 2022 05:33:37
%S A303299 0,1,19,22,58,63,117,124,196,205,295,306,414,427,553,568,712,729,891,
%T A303299 910,1090,1111,1309,1332,1548,1573,1807,1834,2086,2115,2385,2416,2704,
%U A303299 2737,3043,3078,3402,3439,3781,3820,4180,4221,4599,4642,5038,5083,5497,5544,5976,6025,6475,6526,6994,7047,7533,7588
%N A303299 Generalized 22-gonal (or icosidigonal) numbers: m*(10*m - 9) with m = 0, +1, -1, +2, -2, +3, -3, ...
%C A303299 Partial sums of A317318. - _Omar E. Pol_, Jul 28 2018
%C A303299 Exponents in expansion of Product_{n >= 1} (1 + x^(20*n-19))*(1 + x^(20*n-1))*(1 - x^(20*n)) = 1 + x + x^19 + x^22 + x^58 + .... - _Peter Bala_, Dec 10 2020
%H A303299 Colin Barker, <a href="/A303299/b303299.txt">Table of n, a(n) for n = 0..1000</a>
%H A303299 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A303299 From _Colin Barker_, Jun 23 2018: (Start)
%F A303299 G.f.: x*(1 + 18*x + x^2) / ((1 - x)^3*(1 + x)^2).
%F A303299 a(n) = (5*n^2 + 9*n)/2 for n even.
%F A303299 a(n) = (5*n^2 + n - 4)/2 for n odd.
%F A303299 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4.
%F A303299 (End)
%F A303299 Sum_{n>=1} 1/a(n) = (10 + 9*sqrt(5+2*sqrt(5))*Pi)/81. - _Amiram Eldar_, Mar 01 2022
%p A303299 a:= n-> (m-> m*(10*m-9))(-ceil(n/2)*(-1)^n):
%p A303299 seq(a(n), n=0..60); # _Alois P. Heinz_, Jun 23 2018
%t A303299 CoefficientList[ Series[-x (x^2 + 18x + 1)/((x - 1)^3 (x + 1)^2), {x, 0, 50}], x] (* or *)LinearRecurrence[{1, 2, -2, -1, 1}, {0, 1, 19, 22, 58}, 51] (* _Robert G. Wilson v_, Jul 28 2018 *)
%t A303299 nn=30; Sort[Table[n (10 n - 9), {n, -nn, nn}]] (* _Vincenzo Librandi_, Jul 29 2018 *)
%o A303299 (PARI) a(n) = n++; my(m = (-1) ^ n * (n >> 1)); m * (10 * m - 9) \\ _David A. Corneth_, Jun 23 2018
%o A303299 (PARI) concat(0, Vec(x*(1 + 18*x + x^2) / ((1 - x)^3*(1 + x)^2) + O(x^60))) \\ _Colin Barker_, Jun 23 2018
%Y A303299 Cf. A051874, A317318.
%Y A303299 Sequences of generalized k-gonal numbers: A001318 (k=5), A000217 (k=6), A085787 (k=7), A001082 (k=8), A118277 (k=9), A074377 (k=10), A195160 (k=11), A195162 (k=12), A195313 (k=13), A195818 (k=14), A277082 (k=15), A274978 (k=16), A303305 (k=17), A274979 (k=18), A303813 (k=19), A218864 (k=20), A303298 (k=21), this sequence (k=22), A303303 (k=23), A303814 (k=24), A303304 (k=25), A316724 (k=26), A316725 (k=27), A303812 (k=28), A303815 (k=29), A316729 (k=30).
%K A303299 nonn,easy
%O A303299 0,3
%A A303299 _Omar E. Pol_, Jun 23 2018