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 A029007 #28 Jul 08 2025 19:00:52
%S A029007 1,1,2,2,4,5,7,8,11,13,17,19,24,27,33,37,44,49,57,63,73,80,91,99,112,
%T A029007 122,136,147,163,176,194,208,228,244,266,284,308,328,354,376,405,429,
%U A029007 460,486,520,549,585,616,655,689
%N A029007 Expansion of 1/((1-x)(1-x^2)(1-x^4)(1-x^5)).
%C A029007 Partitions of n into parts 1, 2, 4 and 5. - _David Neil McGrath_, Sep 14 2014
%H A029007 Robert Israel, <a href="/A029007/b029007.txt">Table of n, a(n) for n = 0..10000</a>
%H A029007 Xiangyu Ding and Lisa Hui Sun, <a href="https://arxiv.org/abs/2403.11608">Truncated theta series from the Bailey lattice</a>, arXiv:2403.11608 [math.CO], 2024. See p. 18.
%H A029007 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,1,0,-2,0,1,-1,1,1,-1).
%F A029007 a(0)=1, a(1)=1, a(2)=2, a(3)=2, a(4)=4, a(5)=5, a(6)=7, a(7)=8, a(8)=11, a(9)=13, a(10)=17, a(11)=19, a(n)=a(n-1)+a(n-2)-a(n-3)+a(n-4)- 2*a(n-6)+ a(n-8)-a(n-9)+a(n-10)+a(n-11)-a(n-12). - _Harvey P. Dale_, Dec 06 2013
%F A029007 a(n) = floor((2*n^3+36*n^2+193*n+525)/480+(n+1)*(-1)^n/32). - _Tani Akinari_, Sep 30 2014
%F A029007 Euler transform of length 5 sequence [ 1, 1, 0, 1, 1]. - _Michael Somos_, Sep 30 2014
%F A029007 a(n) = -a(-12-n) for all n in Z. - _Michael Somos_, Sep 30 2014
%F A029007 0 = a(n) - a(n+1) - a(n+5) + a(n+6) for all odd n in Z. - _Michael Somos_, Sep 30 2014
%F A029007 0 = a(n) - a(n+1) - a(n+5) + a(n+6) - floor((n+10)/4) for all even n in Z. - _Michael Somos_, Sep 30 2014
%e A029007 There are 7 partitions of 6 from 1,2,4 and 5. These are (51)(42)(411)(222)(2211)(21111)(111111). - _David Neil McGrath_, Sep 14 2014
%e A029007 G.f. = 1 + x + 2*x^2 + 2*x^3 + 4*x^4 + 5*x^5 + 7*x^6 + 8*x^7 + 11*x^8 + ...
%p A029007 f:= gfun[rectoproc]({a(0)=1, a(1)=1, a(2)=2, a(3)=2, a(4)=4, a(5)=5, a(6)=7, a(7)=8, a(8)=11, a(9)=13, a(10)=17, a(11)=19, a(n)=a(n-1)+a(n-2)-a(n-3)+a(n-4)- 2*a(n-6)+ a(n-8)-a(n-9)+a(n-10)+a(n-11)-a(n-12)},a(n)):
%p A029007 seq(f(n),n=0..100); # _Robert Israel_, Sep 14 2014
%t A029007 CoefficientList[Series[1/((1-x)(1-x^2)(1-x^4)(1-x^5)),{x,0,50}],x] (* or *) LinearRecurrence[{1,1,-1,1,0,-2,0,1,-1,1,1,-1},{1,1,2,2,4,5,7,8,11,13,17,19},50] (* _Harvey P. Dale_, Dec 06 2013 *)
%o A029007 (PARI) a(n)=my(v=apply(u->for(i=1,#u,if(u[i]==3,return(0)));1,partitions(n,5)));sum(i=1,#v,v[i]) \\ _Charles R Greathouse IV_, Sep 15 2014
%K A029007 nonn,easy
%O A029007 0,3
%A A029007 _N. J. A. Sloane_