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 A153126 #22 Aug 23 2022 09:50:22
%S A153126 1,6,18,33,55,80,112,147,189,234,286,341,403,468,540,615,697,782,874,
%T A153126 969,1071,1176,1288,1403,1525,1650,1782,1917,2059,2204,2356,2511,2673,
%U A153126 2838,3010,3185,3367,3552,3744,3939,4141,4346,4558,4773,4995,5220,5452
%N A153126 Sums of rows of the triangle in A153125.
%C A153126 Sequence found by reading the line from 1, in the direction 1, 6,..., and the same line from 1, in the direction 1, 18,..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. Line perpendicular to the main axis A195015 in the same spiral. - _Omar E. Pol_, Oct 14 2011
%H A153126 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A153126 a(n) = n*(5*n+7)/2 + 1 - n mod 2.
%F A153126 a(n) = Sum_{k=1..n+1} A153125(n+1,k).
%F A153126 a(2*n) = A033571(n); a(2*n+1) = A153127(n).
%F A153126 a(n) = A000566(n+1) - n mod 2.
%F A153126 From _Colin Barker_, Jul 07 2012: (Start)
%F A153126 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
%F A153126 G.f.: (1+4*x+6*x^2-x^3)/((1-x)^3*(1+x)). (End)
%F A153126 Sum_{n>=0} 1/a(n) = 5/7 + 2*sqrt(1+2/sqrt(5))*Pi/21 + 2*sqrt(5)*log(phi)/21 + 5*log(5)/21 - 8*log(2)/21, where phi is the golden ratio (A001622). - _Amiram Eldar_, Aug 23 2022
%t A153126 LinearRecurrence[{2,0,-2,1},{1,6,18,33},50] (* _Harvey P. Dale_, Apr 13 2014 *)
%o A153126 (PARI) a(n)=n*(5*n+7)/2 + 1 - n%2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A153126 Cf. A000566, A001622, A033571, A153125, A153127.
%K A153126 nonn,easy
%O A153126 0,2
%A A153126 _Reinhard Zumkeller_, Dec 20 2008