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 A051263 #26 Jun 09 2025 00:29:27
%S A051263 1,1,1,3,3,4,7,7,9,13,14,17,22,24,28,35,38,43,52,56,63,74,79,88,101,
%T A051263 108,119,134,143,156,174,185,200,221,234,252,276,291,312,339,357,381,
%U A051263 411,432,459,493,517,547,585,612,646,688,718,756,802,836,878,928,966
%N A051263 Expansion of 1/((1-x)*(1-x^3)^2*(1-x^5)).
%C A051263 A two-way infinite sequences which is palindromic (up to sign). - _Michael Somos_, Mar 21 2003
%H A051263 <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%H A051263 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,1,-2,1,-2,2,0,1,-1).
%F A051263 G.f.: 1 / ((1 - x) * (1 - x^3)^2 * (1 - x^5)).
%F A051263 a(-12 - n) = -a(n). a(n) = a(n-1) + 2*a(n-3) - 2*a(n-4) + a(n-5) - 2*a(n-6) + a(n-7) - 2*a(n-8) + 2*a(n-9) + a(n-11) - a(n-12). - _Michael Somos_, Mar 21 2003
%F A051263 A029153(n) = a(floor(n/2) - mod(n,2)) = a(A028242(n - 2)). - _Michael Somos_, Mar 21 2003
%F A051263 a(n) = 1 + [(n mod 15)=6] + floor((n^3+18*n^2+(87+30*[(n mod 3)=0])*n)/270) where [] is Iverson bracket. - _Hoang Xuan Thanh_, Jun 06 2025
%o A051263 (PARI) {a(n) = if( n<-11, -a(-12 - n), if( n<0, 0, polcoeff( 1 / ((1 - x) * (1 - x^3)^2 * (1 - x^5)) + x * O(x^n),n)))} /* _Michael Somos_, Mar 21 2003 */
%Y A051263 Cf. A028242, A028288, A029153.
%K A051263 nonn,easy
%O A051263 0,4
%A A051263 _N. J. A. Sloane_