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 A228494 #19 May 21 2025 17:03:38
%S A228494 0,0,0,1,2,3,4,7,12,17,24,36,54,77,108,155,222,312,436,612,858,1194,
%T A228494 1656,2298,3184,4397,6060,8346,11480,15762,21612,29607,40518,55385,
%U A228494 75632,103197,140692,191647,260856,354814,482290,655131,889364,1206649,1636218
%N A228494 The number of 3-length segments in all possible covers of L-length line by these segments with allowed gaps < 3.
%C A228494 Related with the number of all possible covers of L-length line segment by 3-length line segments with allowed gaps < 3 (A228362).
%H A228494 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,2,2,-1,-2,-3,-2,-1)
%F A228494 G.f.: x^3*(x^2+x+1)^2/((x^2+1)*(x^3+x^2-1))^2.
%t A228494 c[k_, l_, m_] := Sum[(-1)^i Binomial[k - 1 - i*l, m - 1] Binomial[m, i], {i, 0, Floor[(k - m)/l]}]; a[L_, l_, m_] := Sum[Binomial[m + 1, m + 1 - j]*c[L - l*m, l - 1, j], {j, 0, m + 1}]; sa[L_, l_] := Sum[j*a[L, l, j], {j, 1, Ceiling[L/l]}];Table[sa[j, 3], {j, 0, 100}]
%t A228494 CoefficientList[Series[x^3(x^2+x+1)^2/(x^5+x^4+x^3-1)^2,{x, 0, 100}], x]
%t A228494 LinearRecurrence[{0,0,2,2,2,-1,-2,-3,-2,-1},{0,0,0,1,2,3,4,7,12,17},50] (* _Harvey P. Dale_, May 21 2025 *)
%o A228494 (PARI) concat([0,0,0], Vec(x^3*(x^2+x+1)^2/((x^2+1)*(x^3+x^2-1))^2+O(x^66))) \\ _Joerg Arndt_, Aug 23 2013
%Y A228494 Cf. A228362, A228364.
%K A228494 nonn,easy
%O A228494 0,5
%A A228494 _Philipp O. Tsvetkov_, Aug 23 2013