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 A030503 #19 Jul 09 2020 11:51:38 %S A030503 2,4,8,13,19,27,36,46,58,71,85,101,118,136,156,177,199,223,248,274, %T A030503 302,331,361,393,426,460,496,533,571,611,652,694,738,783,829,877,926, %U A030503 976,1028,1081,1135,1191,1248,1306,1366,1427,1489,1553,1618 %N A030503 Graham-Sloane-type lower bound on the size of a ternary (n,3,3) constant-weight code. %H A030503 Robert Israel, <a href="/A030503/b030503.txt">Table of n, a(n) for n = 3..10000</a> %H A030503 M. Svanstrom, <a href="https://doi.org/10.1109/18.623164">A lower bound for ternary constant weight codes</a>, IEEE Trans. on Information Theory, Vol. 43, pp. 1630-1632, Sep. 1997. %H A030503 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1). %F A030503 a(n) = ceiling(binomial(n, w) * 2^w / (2*n + 1)) with w=3. %F A030503 Conjectures from _Colin Barker_, Aug 02 2019: (Start) %F A030503 G.f.: x^3*(2 + 2*x^2 - x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)). %F A030503 a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) for n>7. %F A030503 (End) %F A030503 From _Robert Israel_, Jul 09 2020: (Start) %F A030503 Conjectures confirmed. %F A030503 a(n) = (2*n^2-7*n+8)/3 if n == 1 (mod 3), otherwise a(n) = (2*n^2-7*n+9)/3. %F A030503 (End) %p A030503 g:= n -> (2*n^2-7*n+`if`(n mod 3 = 1, 8, 9))/3: %p A030503 map(g, [$3..100]); # _Robert Israel_, Jul 09 2020 %K A030503 nonn %O A030503 3,1 %A A030503 Mattias Svanstrom (mattias(AT)isy.liu.se)