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 A239322 #36 Feb 06 2023 14:21:46 %S A239322 0,1,1,-5,-11,61,211,-1385,-6551,50521,303271,-2702765,-19665491, %T A239322 199360981,1704396331,-19391512145,-190473830831,2404879675441, %U A239322 26684005437391,-370371188237525 %N A239322 Interleave (-1)^n*(A000182(n+1) - A000364(n)), -A028296(n+1). %C A239322 Difference table of a(n): %C A239322 0, 1, 1, -5, -11, 61, 211, -1385,... %C A239322 1, 0, -6, -6, 72, 150, -1596,... %C A239322 -1, -6, 0, 78, 78, -1746,... %C A239322 -5, -6, 78, 0, -1824,... %C A239322 11, 72, 78, -1824,... %C A239322 61, -150, -1746,... %C A239322 -211, -1596,... %C A239322 -1385,... %C A239322 etc. %C A239322 a(n) is an autosequence (its inverse binomial transform is the signed sequence) of the first kind (its main diagonal is A000004=0's and the first two upper diagonal are the same). Like A000045(n). %C A239322 Note that e(n) = A000111(n+1) - A000111(n) = 0, 0, 1, 3, 11, 45, 211,... is not in the OEIS. a(2n) = (-1)*(n+1)*e(2n). %C A239322 Antidiagonals upon A000004: %C A239322 1, %C A239322 1, %C A239322 -6, -5, %C A239322 -6, -11, %C A239322 78, 72, 61, %C A239322 78, 150, 211, %C A239322 Row sum: 1, 1, -11, -17, 211, 439,... . %C A239322 b(n) = a(n) mod 9 = 0 followed by period 6: repeat 1, 1, 4, 7, 7, 4 is also an autosequence of the first kind. %e A239322 a(0)=1-1=0, a(1)=-(-1)=1, a(2)=2-1=1, a(3)=-5, a(4)=-(16-5)=-11. %Y A239322 Cf. Zig (A000364) and Zag (A000182) give Euler A000111(n). %K A239322 sign %O A239322 0,4 %A A239322 _Paul Curtz_, Mar 28 2014