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 A381196 #36 Mar 05 2025 20:44:00 %S A381196 1,29,97,205,353,541,769,1037,1345,1693,2081,2509,2977,3485,4033,4621, %T A381196 5249,5917,6625,7373,8161,8989,9857,10765,11713,12701,13729,14797, %U A381196 15905,17053,18241,19469,20737,22045,23393,24781,26209,27677,29185,30733,32321,33949 %N A381196 Stellated octagon numbers: a(n) = 20*n^2 + 8*n + 1. %C A381196 Sequence found by reading the line from 1, in the direction 1, 29, ..., in the square spiral whose vertices are the generalized dodecagonal numbers A195162. - _Omar E. Pol_, Feb 17 2025 %H A381196 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A381196 a(n) = (4*n + 1)^2 + 4*n^2. %F A381196 a(n) = A001844(3*n - 2) + 4*A000217(n - 1). %F A381196 a(n) = 4 * A168668(n) + 1. %F A381196 a(n) = A016814(n) + A016742(n). %F A381196 G.f.: (13*x^2+26*x+1) / (1-x)^3. %F A381196 E.g.f.: exp(x) * (1 + 28*x + 20*x^2). - _Stefano Spezia_, Feb 23 2025 %e A381196 Illustration of initial terms: %e A381196 . %e A381196 . o %e A381196 . o o o %e A381196 . o o o o o o o o o %e A381196 . o o o o o o o o o o %e A381196 . o o o o o o o o o o o o o o %e A381196 . o o o o o o o o o o o o o o o o %e A381196 . o o o o o o o o o o o o o o o o o o o o o %e A381196 . o o o o o o o o o o o o o o o o %e A381196 . o o o o o o o o o o o o o o %e A381196 . o o o o o o o o o o %e A381196 . o o o o o o o o o %e A381196 . o o o %e A381196 . o %e A381196 . %e A381196 . 1 29 97 %t A381196 a[n_] := 20*n^2 + 8*n + 1; Array[a, 42, 0] (* _Amiram Eldar_, Feb 17 2025 *) %Y A381196 Cf. A000217, A001844, A016742, A016814, A168668, A195162. %K A381196 nonn,easy %O A381196 0,2 %A A381196 _Aaron David Fairbanks_, Feb 16 2025