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 A317324 #35 Dec 11 2024 06:29:09
%S A317324 0,1,24,3,48,5,72,7,96,9,120,11,144,13,168,15,192,17,216,19,240,21,
%T A317324 264,23,288,25,312,27,336,29,360,31,384,33,408,35,432,37,456,39,480,
%U A317324 41,504,43,528,45,552,47,576,49,600,51,624,53,648,55,672,57,696,59,720,61,744,63,768,65,792,67,816,69
%N A317324 Multiples of 24 and odd numbers interleaved.
%C A317324 Partial sums give the generalized 28-gonal numbers (A303812).
%C A317324 a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 28-gonal numbers.
%H A317324 Colin Barker, <a href="/A317324/b317324.txt">Table of n, a(n) for n = 0..1000</a>
%H A317324 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A317324 a(2n) = 24*n, a(2n+1) = 2*n + 1.
%F A317324 G.f.: x*(1 + 24*x + x^2)/((1-x)^2*(1+x)^2). - _Vincenzo Librandi_, Jul 28 2018
%F A317324 a(n) = 2*a(n-2) - a(n-4) for n>3. - _Colin Barker_, Jul 29 2018
%F A317324 Multiplicative with a(2^e) = 3*2^(e+2), and a(p^e) = p^e for an odd prime p. - _Amiram Eldar_, Oct 14 2023
%F A317324 Dirichlet g.f.: zeta(s-1) * (1 + 11*2^(1-s)). - _Amiram Eldar_, Oct 26 2023
%t A317324 Table[If[EvenQ[n], 24 (n/2), n], {n, 0, 70}] (* _Vincenzo Librandi_, Jul 28 2018 *)
%t A317324 With[{nn=40},Riffle[24*Range[0,nn],2*Range[0,nn]+1]] (* or *) LinearRecurrence[ {0,2,0,-1},{0,1,24,3},80] (* _Harvey P. Dale_, Jul 06 2019 *)
%o A317324 (Magma) &cat[[24*n, 2*n + 1]: n in [0..30]]; // _Vincenzo Librandi_, Jul 28 2018
%o A317324 (PARI) concat(0, Vec(x*(1 + 24*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ _Colin Barker_, Jul 29 2018
%Y A317324 Cf. A008606 and A005408 interleaved.
%Y A317324 Column 24 of A195151.
%Y A317324 Sequences whose partial sums give the generalized k-gonal numbers: A026741 (k=5), A001477 (k=6), zero together with A080512 (k=7), A022998 (k=8), A195140 (k=9), zero together with A165998 (k=10), A195159 (k=11), A195161 (k=12), A195312 (k=13), A195817 (k=14).
%Y A317324 Cf. A303812.
%K A317324 nonn,easy,mult
%O A317324 0,3
%A A317324 _Omar E. Pol_, Jul 25 2018