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 A202391 #28 Feb 18 2025 03:55:00 %S A202391 5,39,237,1391,8117,47319,275805,1607519,9369317,54608391,318281037, %T A202391 1855077839,10812186005,63018038199,367296043197,2140758220991, %U A202391 12477253282757,72722761475559,423859315570605,2470433131948079 %N A202391 Indices of the smallest of four consecutive triangular numbers summing up to a square. %C A202391 Positive integers n such that A000217(n) + A000217(n + 1) + A000217(n + 2) + A000217(n + 3) is a square (=A075870(n+1)^2). %H A202391 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,1). %F A202391 a(n) = A002315(n) - 2. %F A202391 G.f.: x*(1+x)*(x-5) / ( (x-1)*(1-6*x+x^2) ). - _R. J. Mathar_, Dec 19 2011 %F A202391 a(n+2) = 6*a(n+1) - a(n) + 8; a(n+3) = 7*a(n+2) - 7*a(n+1) + a(n); a(n+1) = (-4 + (7 + 5*r)*(3 + 2*r)^n + (7 - 5*r)*(3 - 2*r)^n)/2 where r = sqrt(2). - _Paul Weisenhorn_, Jan 13 2013 %Y A202391 Cf. A176541, A176542, A165517, A116476, A075870 %K A202391 nonn %O A202391 1,1 %A A202391 _Max Alekseyev_, Dec 18 2011