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 A035937 #41 Jan 12 2019 20:43:42
%S A035937 1,0,1,1,2,2,3,3,5,6,8,9,13,14,19,22,28,32,41,47,59,68,83,96,117,134,
%T A035937 161,186,221,254,301,344,405,464,541,619,720,820,949,1081,1245,1414,
%U A035937 1624,1840,2106,2384,2717,3070,3492,3936,4464,5026,5684,6388,7210,8088
%N A035937 Number of partitions in parts not of the form 7k, 7k+1 or 7k-1. Also number of partitions with no part of size 1 and differences between parts at distance 2 are greater than 1.
%C A035937 Case k=3, i=1 of Gordon Theorem.
%D A035937 G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%H A035937 Jean-François Alcover and Vaclav Kotesovec, <a href="/A035937/b035937.txt">Table of n, a(n) for n = 0..1000</a> (first 99 terms from Jean-François Alcover)
%F A035937 Expansion of f(-x, -x^6) / f(-x, -x^2) in powers of x where f() is Ramanujan's general theta function.
%F A035937 Euler transform of period 7 sequence [ 0, 1, 1, 1, 1, 0, 0, ...]. - _Michael Somos_, Dec 30 2014
%F A035937 G.f.: 1 / (Product_{k>0} (1 - x^(7*k - 5)) * (1 - x^(7*k - 4)) * (1 - x^(7*k - 3)) * (1 - x^(7*k - 2))). - _Michael Somos_, Dec 30 2014 [corrected by _Vaclav Kotesovec_, Nov 12 2015]
%F A035937 G.f.: (Product_{k>1} (1 - x^k)) * (Sum_{k>0} x^(2*k + 2*k^2) / (Product_{i=1..k} (1 - x^(2*i)) * (1 + x^(2*i)) * (1 + x^(2*i+1)))). - _Michael Somos_, Dec 31 2014
%F A035937 a(n) ~ 2^(1/4) * sin(Pi/7) * exp(2*Pi*sqrt(2*n/21)) / (3^(1/4) * 7^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, Nov 12 2015
%e A035937 G.f. = 1 + x^2 + x^3 + 2*x^4 + 2*x^5 + 3*x^6 + 3*x^7 + 5*x^8 + 6*x^9 + ...
%e A035937 G.f. = q^17 + q^101 + q^143 + 2*q^185 + 2*q^227 + 3*q^269 + 3*q^311 + ...
%p A035937 with (numtheory):
%p A035937 GordonsTheorem := proc(A, n) local L,M,m,i,s,d;
%p A035937 L := []; M := []; m := nops(A);
%p A035937 for i in [$1..n] do
%p A035937 s := add(d*A[((d-1) mod m) + 1], d = divisors(i));
%p A035937 L := [op(L), s];
%p A035937 s := s + add(L[d]*M[i-d], d = [$1..i-1]);
%p A035937 M := [op(M), s/i];
%p A035937 od; M end:
%p A035937 A035937_list := n -> GordonsTheorem([0, 1, 1, 1, 1, 0, 0], n):
%p A035937 A035937_list(40); # _Peter Luschny_, Jan 22 2012
%t A035937 f[max_][a_, b_] := Sum[a^(n*(n+1)/2)*b^(n*(n-1)/2), {n, -max, max}]; a[n_, max_] := a[n, max] = SeriesCoefficient[f[max][-x, -x^6]/f[max][-x, -x^2], {x, 0, n}]; a[n_] := (a[n, 2]; a[n, max = 3]; While[a[n, max] != a[n, max-1], max++]; a[n, max]); Table[a[n], {n, 0, 99}] (* _Jean-François Alcover_, Jan 13 2014 *)
%t A035937 a[ n_] := SeriesCoefficient[ 1 / Product[ (1 - x^(7 k - 2)) (1 - x^(7 k - 3)) (1 - x^(7 k - 4)) (1 - x^(7 k - 5)), {k, Ceiling[n/7]}], {x, 0, n}]; (* _Michael Somos_, Dec 30 2014 *)
%t A035937 a[ n_] := SeriesCoefficient[ 1 / (QPochhammer[ x^2, x^7] QPochhammer[ x^3, x^7] QPochhammer[ x^4, x^7] QPochhammer[ x^5, x^7] ), {x, 0, n}]; (* _Michael Somos_, Dec 30 2014 *)
%o A035937 (Sage)
%o A035937 def GordonsTheorem(A, n) :
%o A035937 L = []; M = [];
%o A035937 m = len(A)
%o A035937 for i in range(n) :
%o A035937 s = sum(d*A[(d-1) % m] for d in divisors(i+1))
%o A035937 L.append(s)
%o A035937 s = s + sum(L[d-1]*M[i-d] for d in (1..i))
%o A035937 M.append(s/(i+1))
%o A035937 return M
%o A035937 def A035937_list(len) : return GordonsTheorem([0, 1, 1, 1, 1, 0, 0], len)
%o A035937 A035937_list(40) # Peter Luschny, Jan 22 2012
%o A035937 (PARI) {a(n) = my(A); if( n<0, 0, polcoeff( 1 / prod( k=1, n, 1 - [0, 0, 1, 1, 1, 1, 0][k%7 + 1] * x^k, 1 + x * O(x^n)), n))}; /* _Michael Somos_, Dec 30 2014 */
%Y A035937 Cf. A035938, A035939.
%K A035937 nonn,easy
%O A035937 0,5
%A A035937 _Olivier Gérard_