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 A378622 #6 Dec 14 2024 10:51:20
%S A378622 1,1,0,1,0,0,2,1,1,1,2,0,-1,-2,-3,3,1,1,2,4,7,4,1,0,-1,-3,-7,-14,5,1,
%T A378622 0,0,1,4,11,25,6,1,0,0,0,-1,-5,-16,-41,8,2,1,1,1,1,2,7,23,64,10,2,0,
%U A378622 -1,-2,-3,-4,-6,-13,-36,-100,12,2,0,0,1,3,6,10,16,29,65,165
%N A378622 Array read by antidiagonals downward where A(n,k) is the n-th term of the k-th differences of the strict partition numbers A000009.
%e A378622 As a table (read by antidiagonals downward):
%e A378622 n=0: n=1: n=2: n=3: n=4: n=5: n=6: n=7: n=8:
%e A378622 ----------------------------------------------------------
%e A378622 k=0: 1 1 1 2 2 3 4 5 6
%e A378622 k=1: 0 0 1 0 1 1 1 1 2
%e A378622 k=2: 0 1 -1 1 0 0 0 1 0
%e A378622 k=3: 1 -2 2 -1 0 0 1 -1 0
%e A378622 k=4: -3 4 -3 1 0 1 -2 1 1
%e A378622 k=5: 7 -7 4 -1 1 -3 3 0 -3
%e A378622 k=6: -14 11 -5 2 -4 6 -3 -3 7
%e A378622 k=7: 25 -16 7 -6 10 -9 0 10 -14
%e A378622 k=8: -41 23 -13 16 -19 9 10 -24 24
%e A378622 k=9: 64 -36 29 -35 28 1 -34 48 -34
%e A378622 As a triangle (read by rows):
%e A378622 1
%e A378622 1 0
%e A378622 1 0 0
%e A378622 2 1 1 1
%e A378622 2 0 -1 -2 -3
%e A378622 3 1 1 2 4 7
%e A378622 4 1 0 -1 -3 -7 -14
%e A378622 5 1 0 0 1 4 11 25
%e A378622 6 1 0 0 0 -1 -5 -16 -41
%e A378622 8 2 1 1 1 1 2 7 23 64
%t A378622 nn=20;
%t A378622 t=Table[Take[Differences[PartitionsQ/@Range[0,2nn],k],nn],{k,0,nn}];
%t A378622 Table[t[[j,i-j+1]],{i,nn/2},{j,i}]
%Y A378622 Rows are: A000009 (k=0), A087897 (k=1, without first term), A378972 (k=2).
%Y A378622 For primes we have A095195 or A376682.
%Y A378622 For partitions we have A175804.
%Y A378622 First column is A293467 (up to sign).
%Y A378622 For composites we have A377033.
%Y A378622 For squarefree numbers we have A377038.
%Y A378622 For nonsquarefree numbers we have A377046.
%Y A378622 For prime powers we have A377051.
%Y A378622 Position of first zero in each row is A377285.
%Y A378622 Triangle's row-sums are A378970, absolute A378971.
%Y A378622 A000009 counts strict integer partitions, differences A087897, A378972.
%Y A378622 A000041 counts integer partitions, differences A002865, A053445.
%Y A378622 Cf. A047966, A098859, A225486, A325244, A325282.
%Y A378622 Cf. A008284, A116608, A325242, A225485 or A325280.
%K A378622 sign,tabl
%O A378622 0,7
%A A378622 _Gus Wiseman_, Dec 13 2024