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 A127948 #8 Jun 20 2025 12:42:12 %S A127948 1,0,2,-1,1,3,-2,0,2,4,-3,-1,1,3,5,-4,-2,0,2,4,6,-5,-3,-1,1,3,5,7,-6, %T A127948 -4,-2,0,2,4,6,8,-7,-5,-3,-1,1,3,5,7,9,-8,-6,-4,-2,0,2,4,6,8,10 %N A127948 Triangle, A004736 * A127899. %C A127948 Row sums = n A127899 * A004736 = A002024 %F A127948 A004736 * A127899 as infinite lower triangular matrices; where A004736 = (1; 2,1; 3,2,1;...). %F A127948 From _Boris Putievskiy_, Jan 15 2013: (Start) %F A127948 a(n) = 2*A000027(n)-A002024(n)^2, n > 0, %F A127948 a(n) = 2*n-(t+1)^2, where t = floor((-1+sqrt(8*n-7))/2) n > 0. (End) %e A127948 First few rows of the triangle are: %e A127948 1; %e A127948 0, 2; %e A127948 -1, 1, 3; %e A127948 -2, 0, 2, 4; %e A127948 -3, -1, 1, 3, 5; %e A127948 -4, -2, 0, 2, 4, 6; %e A127948 -5, -3, -1, 1, 3, 5, 7; %e A127948 ... %o A127948 (Python) %o A127948 from math import isqrt %o A127948 def A127948(n): return (m:=n<<1)-(isqrt(m<<2)+1>>1)**2 # _Chai Wah Wu_, Jun 20 2025 %Y A127948 Cf. A127899, A004736, A002024. %K A127948 tabl,sign %O A127948 0,3 %A A127948 _Gary W. Adamson_, Feb 09 2007