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 A098098 #35 Dec 17 2022 02:54:42
%S A098098 1,2,3,4,5,8,7,8,9,10,14,12,16,14,15,20,17,18,19,24,26,22,23,28,25,32,
%T A098098 32,28,29,30,38,32,33,40,40,44,42,38,39,40,57,42,43,44,45,62,47,56,49,
%U A098098 56,62,52,53,60,64,68,64,58,59,60,74,72,70,64,65,80,67,76,80,70,93,72
%N A098098 a(n) = sigma(6*n+5)/6.
%C A098098 Euler transform of period 6 sequence [2, 0, 0, 0, 2, -4, ...].
%C A098098 Expansion of q^(-5/6) * (eta(q)^-1 * eta(q^2) * eta(q^3) * eta(q^6))^2 in powers of q. - _Michael Somos_, Sep 16 2004
%C A098098 2*a(n) is the number of bipartitions of 2*n+1 that are 3-cores. See Baruah and Nath. - _Michel Marcus_, Apr 13 2020
%H A098098 Ivan Neretin, <a href="/A098098/b098098.txt">Table of n, a(n) for n = 0..10000</a>
%H A098098 Nayandeep Deka Baruah and Kallol Nath, <a href="https://doi.org/10.1016/j.jnt.2014.10.010">Infinite families of arithmetic identities and congruences for bipartitions with 3-cores</a>, Journal of Number Theory, Volume 149, April 2015, Pages 92-104.
%F A098098 G.f.: (Product_{k>0} (1 + x^k) * (1 - x^(3*k)) * (1 - x^(6*k)))^2. - _Michael Somos_, Sep 16 2004
%F A098098 From _Michael Somos_, Jul 09 2018: (Start)
%F A098098 G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = (t/i)^2 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A252650. -
%F A098098 Convolution square of A121444.
%F A098098 A232343(2*n) = (-1)^n * A258831(n) = A000203(6*n + 4) = a(n). A033686(2*n) = -A134079(2*n + 1) = 2 * a(n). A121443(6*n + 5) = A133739(6*n + 5) = A232356(6*n + 5) = A134077(3*n + 2) = 6 * a(n). A125514(6*n + 5) = 24 * a(n). A134078(6*n + 5) = -36 * a(n). A186100(6*n + 5) = -72 * a(n). (End)
%F A098098 From _Amiram Eldar_, Dec 16 2022: (Start)
%F A098098 a(n) = A000203(A016969(n))/6.
%F A098098 Sum_{k=1..n} a(k) = (Pi^2/18) * n^2 + O(n*log(n)). (End)
%e A098098 G.f. =1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 8*x^5 + 7*x^6 + 8*x^7 + 9*x^8 + 10*x^9 + ...
%e A098098 G.f. = q^5 + 2*q^11 + 3*q^17 + 4*q^23 + 5*q^29 + 8*q^35 + 7*q^41 + 8*q^47 + 9*q^53 + ...
%t A098098 Table[DivisorSigma[1, 6 n + 5]/6, {n, 0, 71}] (* _Ivan Neretin_, Apr 30 2016 *)
%o A098098 (PARI) a(n) = sigma(6*n + 5)/6
%o A098098 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A) * eta(x^3 + A) * eta(x^6 + A) / eta(x + A))^2, n))} /* _Michael Somos_, Sep 16 2004 */
%o A098098 (Magma) Basis( ModularForms( Gamma0( 36), 2), 432)[6]; /* _Michael Somos_, Jul 09 2018 */
%Y A098098 Cf. A000203, A016969, A033686, A097723, A121443, A125514, A133739, A134077, A134078, A134079, A186100, A232343, A232356, A252650, A238831.
%K A098098 easy,nonn
%O A098098 0,2
%A A098098 _Vladeta Jovovic_, Sep 14 2004