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 A129966 #13 May 26 2025 05:17:28
%S A129966 0,1,3,15,21,28,36,45,55,91,105,120,136,153,171,231,253,276,300,325,
%T A129966 351,435,465,496,528,561,595,703,741,780,820,861,903,1035,1081,1128,
%U A129966 1176,1225,1275,1431,1485,1540,1596,1653,1711,1891,1953,2016,2080,2145,2211,2415,2485
%N A129966 Triangular numbers which are differences of squares.
%C A129966 These are the triangular numbers n*(n+1)/2 where n is not congruent to 3 or 4 mod 8. (Since the numbers not the difference of two squares are precisely those congruent to 2 mod 4.) - _Franklin T. Adams-Watters_, Jun 14 2007
%H A129966 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,2,-2,0,0,0,0,-1,1).
%F A129966 G.f.: ( -x^2*(x^2+1)*(x^8+2*x^7+11*x^6+4*x^5-4*x^4+4*x^3+11*x^2+2*x+1) ) / ( (1+x)^2*(1+x+x^2)^2*(x^2-x+1)^2*(x-1)^3 ) with a(n) = +a(n-1) +2*a(n-6) -2*a(n-7) -a(n-12) +a(n-13). - _R. J. Mathar_, Oct 25 2011
%t A129966 With[{n = 100}, Intersection[(#1*((#1 + 1)/2) & ) /@ Range[0, n], Flatten[Outer[ #1^2 - #2^2 &, Range[n], Range[0, n - 1]]]]]
%K A129966 nonn,easy
%O A129966 1,3
%A A129966 Peter Pein (petsie(AT)dordos.net), Jun 14 2007
%E A129966 More terms from _Michel Marcus_, May 26 2025