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 A237047 #13 Feb 17 2014 23:42:42 %S A237047 0,-1,-2,-4,-6,-8,-8,0,28,102,280,680,1544,3368,7152,14912,30706, %T A237047 62672,127124,256744,516952,1038672,2083864,4176576,8365080,16746150, %U A237047 33513608,67055456,134148160,268345208,536754288,1073591680,2147291036,4294721040,8589620784 %N A237047 Number of compositions of n minus the number of overpartitions of n. %C A237047 Note that a(7) = 0 therefore 7 is the only positive integer whose number of compositions equals the number of overpartitions: A011782(7) = A015128(7) = 64. %F A237047 a(n) = A011782(n) - A015128(n). %e A237047 Illustration of a(4) = -6. %e A237047 -------------------------------------------------------- %e A237047 . Compositions of 4 Overpartitions of 4 %e A237047 -------------------------------------------------------- %e A237047 . _ _ _ _ _ _ _ _ %e A237047 1 |_| | | | 1, 1, 1, 1 |.| | | | 1', 1, 1, 1 %e A237047 2 |_ _| | | 2, 1, 1 |_| | | | 1, 1, 1, 1 %e A237047 3 |_| | | 1, 2, 1 | .|.| | 2', 1', 1 %e A237047 4 |_ _ _| | 3, 1 | |.| | 2, 1', 1 %e A237047 5 |_| | | 1, 1, 2 | .| | | 2', 1, 1 %e A237047 6 |_ _| | 2, 2 |_ _| | | 2, 1, 1 %e A237047 7 |_| | 1, 3 | .|.| 3', 1 %e A237047 8 |_ _ _ _| 4 | |.| 3, 1 %e A237047 9 | .| | 3', 1 %e A237047 10 |_ _ _| | 3, 1 %e A237047 11 | .| | 2', 2 %e A237047 12 |_ _| | 2, 2 %e A237047 13 | .| 4' %e A237047 14 |_ _ _ _| 4 %e A237047 . %e A237047 There are 8 compositions of 4 and there are 14 overpartitions of 4, so a(4) = 8 - 14 = -6. %Y A237047 Cf. A011782, A015128, A056823, A230441, A236633, A237044, A237045. %K A237047 sign %O A237047 0,3 %A A237047 _Omar E. Pol_, Feb 02 2014