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 A129895 #21 Feb 23 2019 04:44:29
%S A129895 1,2,3,5,7,9,11,13,15,18,21,25,29,33,37,41,45,50,55,61,67,73,79,85,91,
%T A129895 98,105,113,121,129,137,145,153,162,171,181,191,201,211,221,231,242,
%U A129895 253,265,277,289,301,313,325,338,351,365,379,393,407,421,435,450,465,481
%N A129895 a(1)=1. a(n) = a(n-1) + number of triangular numbers among the first (n-1) terms of the sequence.
%H A129895 Harvey P. Dale, <a href="/A129895/b129895.txt">Table of n, a(n) for n = 1..1000</a>
%H A129895 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -2, 0, 2, 0, -2, 1).
%F A129895 For k=1,3: a(8*n+k) = (4*n+k)*(2*n+1). - _Reinhard Zumkeller_, Dec 20 2007
%F A129895 G.f.: -x*(x^7 - x^6 - x^5 + x^4 + x^3 - x^2 + 1) / ((x-1)^3*(x+1)*(x^4+1)). - _Colin Barker_, Mar 29 2013
%F A129895 a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-5) - 2*a(n-7) + a(n-8); a(1)=1, a(2)=2, a(3)=3, a(4)=5, a(5)=7, a(6)=9, a(7)=11, a(8)=13. - _Harvey P. Dale_, May 16 2014
%p A129895 T := {seq((1/2)*j*(j+1), j = 1 .. 40)}: a[1] := 1; for n from 2 to 60 do a[n] := a[n-1]+nops(`intersect`(T, {seq(a[i], i = 1 .. n-1)})) end do: seq(a[n], n = 1 .. 60); # _Emeric Deutsch_, Jun 21 2007
%t A129895 nxt[{a_,t_}]:=Module[{x=t},{a+t,If[IntegerQ[(Sqrt[8(a+t)+1]-1)/2], x+1, x]}]; Transpose[NestList[nxt,{1,1},70]][[1]] (* or *) LinearRecurrence[ {2,0,-2,0,2,0,-2,1},{1,2,3,5,7,9,11,13},70] (* _Harvey P. Dale_, May 16 2014 *)
%Y A129895 Cf. A097602.
%K A129895 nonn
%O A129895 1,2
%A A129895 _Leroy Quet_, Jun 04 2007
%E A129895 More terms from _Emeric Deutsch_, Jun 21 2007