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 A317311 #48 Dec 11 2024 05:35:34
%S A317311 0,1,11,3,22,5,33,7,44,9,55,11,66,13,77,15,88,17,99,19,110,21,121,23,
%T A317311 132,25,143,27,154,29,165,31,176,33,187,35,198,37,209,39,220,41,231,
%U A317311 43,242,45,253,47,264,49,275,51,286,53,297,55,308,57,319,59,330,61,341,63,352,65,363,67,374,69
%N A317311 Multiples of 11 and odd numbers interleaved.
%C A317311 Partial sums give the generalized 15-gonal numbers (A277082).
%C A317311 a(n) is also the length of the n-th line segment of the rectangular spiral wh0se vertices are the generalized 15-gonal numbers.
%H A317311 Colin Barker, <a href="/A317311/b317311.txt">Table of n, a(n) for n = 0..1000</a>
%H A317311 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A317311 a(2n) = 11*n, a(2n+1) = 2*n + 1.
%F A317311 From _Colin Barker_, Jul 26 2018: (Start)
%F A317311 G.f.: x*(1 + 11*x + x^2) / ((1 - x)^2*(1 + x)^2).
%F A317311 a(n) = 2*a(n-2) - a(n-4) for n>3. (End)
%F A317311 Multiplicative with a(2^e) = 11*2^(e-1), and a(p^e) = p^e for an odd prime p. - _Amiram Eldar_, Oct 14 2023
%F A317311 Dirichlet g.f.: zeta(s-1) * (1 + 9/2^s). - _Amiram Eldar_, Oct 25 2023
%F A317311 a(n) = (13 + 9*(-1)^n)*n/4. - _Aaron J Grech_, Aug 20 2024
%t A317311 {0}~Join~Riffle[2 Range@ # - 1, 11 Range@ #] &@ 35 (* or *)
%t A317311 CoefficientList[Series[x (1 + 11 x + x^2)/((1 - x)^2*(1 + x)^2), {x, 0, 69}], x] (* _Michael De Vlieger_, Jul 26 2018 *)
%t A317311 LinearRecurrence[{0,2,0,-1},{0,1,11,3},90] (* _Harvey P. Dale_, Aug 28 2022 *)
%o A317311 (PARI) concat(0, Vec(x*(1 + 11*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^40))) \\ _Colin Barker_, Jul 26 2018
%Y A317311 Cf. A008593 and A005408 interleaved.
%Y A317311 Column 11 of A195151.
%Y A317311 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 A317311 Cf. A277082.
%K A317311 nonn,mult,easy
%O A317311 0,3
%A A317311 _Omar E. Pol_, Jul 25 2018