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 A025829 #40 Sep 01 2025 11:19:43
%S A025829 1,0,0,1,1,0,1,2,1,1,2,2,2,2,3,3,3,3,4,4,4,5,5,5,6,6,6,7,8,7,8,9,9,9,
%T A025829 10,11,11,11,12,13,13,13,15,15,15,16,17,17,18,19,19,20,21,21,22,23,24,
%U A025829 24,25,26,27,27,28,30,30,30
%N A025829 Expansion of 1/((1-x^3)*(1-x^4)*(1-x^7)).
%C A025829 Partition of n into parts 3, 4, and 7; see A245368 for the compositions. - _David Neil McGrath_, Sep 08 2014
%H A025829 Robert Israel, <a href="/A025829/b025829.txt">Table of n, a(n) for n = 0..10000</a>
%H A025829 F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Sloane/sloane55.html">A slow-growing sequence defined by an unusual recurrence</a>, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
%H A025829 <a href="/index/Ge#Gijswijt">Index entries for sequences related to Gijswijt's sequence</a>
%H A025829 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,1,0,0,0,0,0,-1,-1,0,0,1).
%F A025829 a(n) = a(n-3)+a(n-4)-a(n-10)-a(n-11)+a(n-14). - _David Neil McGrath_, Sep 08 2014
%F A025829 a(n) = floor(((n+1)*(n+13) + 19*(((n+1) mod 3) - (n mod3)))/168 + ((n mod 4)-1)*(3*(n mod 4)-5)/8 + ((n+1) mod 4)/4). - _Hoang Xuan Thanh_, Sep 01 2025
%e A025829 There are 7 partitions of 27 into parts 3,4 and 7. These are (77733)(774333)(744444)(7443333)(4444443)(44433333)(333333333). - _David Neil McGrath_, Sep 08 2014
%p A025829 f:= gfun:-rectoproc({a(0) = 1, a(1) = 0, a(2) = 0, a(3) = 1, a(4) = 1, a(5) = 0, a(6) = 1, a(7) = 2, a(8) = 1, a(9) = 1, a(10) = 2, a(11) = 2, a(12) = 2, a(13) = 2, a(n) = a(n-3)+a(n-4)-a(n-10)-a(n-11)+a(n-14)},a(n),'remember'):
%p A025829 seq(f(n),n=0..100); # _Robert Israel_, Sep 08 2014
%t A025829 LinearRecurrence[{0,0,1,1,0,0,0,0,0,-1,-1,0,0,1}, {1,0,0,1,1,0,1,2,1,1,2,2,2,2}, 80] (* _Jean-François Alcover_, Aug 21 2022 *)
%o A025829 (PARI) a(n)=floor((-2)^(n%3\2)/9-(n%2)*(-1)^(n\2)/4+(3*n^2+42*n+448)/504) \\ _Tani Akinari_, Aug 19 2013
%o A025829 (PARI) Vec(1/((1-x^3)*(1-x^4)*(1-x^7)) + O(x^80)) \\ _Michel Marcus_, Sep 08 2014
%o A025829 (PARI) a(n) = (n^2 +14*n -56*[0,0,1][n%3+1] +21*[8,5,8,9][n%4+1])\168 \\ _Hoang Xuan Thanh_, Sep 01 2025
%K A025829 nonn,easy,changed
%O A025829 0,8
%A A025829 _N. J. A. Sloane_