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 A233329 #25 Sep 08 2022 08:46:06
%S A233329 1,7,21,51,102,186,310,490,735,1065,1491,2037,2716,3556,4572,5796,
%T A233329 7245,8955,10945,13255,15906,18942,22386,26286,30667,35581,41055,
%U A233329 47145,53880,61320,69496,78472,88281,98991,110637,123291,136990,151810,167790,185010,203511
%N A233329 Expansion of (1+4*x+x^2)/((1+x)^2*(1-x)^5).
%C A233329 Sequence is related to enumeration of coronas in A233332.
%C A233329 Conjecture: sequence gives column 1 of A233331 (up to an offset).
%H A233329 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-5,5,1,-3,1).
%F A233329 G.f.: (1+4*x+x^2)/((1+x)^2*(1-x)^5).
%F A233329 a(n) = (2*(n^4+10*n^3+34*n^2+(45+(-1)^(n+1))*n)+37+5*(-1)^(n+1))/32.
%F A233329 a(n) = sum_{j=1..n+1} ( sum_{i=1..j+1} floor(i*j/2) ). - _Wesley Ivan Hurt_, Nov 17 2014
%p A233329 A233329:=n->(2*n^4+20*n^3+68*n^2+90*n+37-2*n*(-1)^n-5*(-1)^n)/32: seq(A233329(n), n=0..50); # _Wesley Ivan Hurt_, Nov 17 2014
%t A233329 CoefficientList[Series[(1 + 4*x + x^2)/((1 + x)^2*(1 - x)^5), {x, 0, 50}], x] (* _Wesley Ivan Hurt_, Nov 17 2014 *)
%t A233329 LinearRecurrence[{3,-1,-5,5,1,-3,1},{1,7,21,51,102,186,310},50] (* _Harvey P. Dale_, Jul 05 2019 *)
%o A233329 (PARI) a(n) = (2*n^4+20*n^3+68*n^2+(90-2*(-1)^n)*n)\/32+1 \\ _Charles R Greathouse IV_, Oct 28 2014
%o A233329 (Magma) [(2*n^4+20*n^3+68*n^2+90*n+37-2*n*(-1)^n-5*(-1)^n)/32 : n in [0..50]]; // _Wesley Ivan Hurt_, Nov 17 2014
%Y A233329 Cf. A076454 (bisection, up to an offset), A233330-A233333.
%K A233329 nonn,easy
%O A233329 0,2
%A A233329 _L. Edson Jeffery_, Jan 06 2014