cp's OEIS Frontend

A378970 Antidiagonal-sums of the array A378622(n,k) = n-th term of k-th differences of strict partition numbers (A000009).

%I A378970 #8 Dec 14 2024 20:30:02
%S A378970 1,1,1,5,-4,18,-20,47,-56,110,-153,309,-532,1045,-1768,2855,-3620,
%T A378970 2928,2927,-20371,62261,-148774,314112,-613835,1155936,-2175658,
%U A378970 4244218,-8753316,19006746,-42471491,95234915,-210395017,453414314,-949507878,1931940045
%N A378970 Antidiagonal-sums of the array A378622(n,k) = n-th term of k-th differences of strict partition numbers (A000009).
%e A378970 Antidiagonal 4 of A378622 is (2, 0, -1, -2, -3), so a(4) = -4.
%t A378970 nn=30;
%t A378970 t=Table[Take[Differences[PartitionsQ/@Range[0,2nn],k],nn],{k,0,nn}];
%t A378970 Total/@Table[t[[j,i-j+1]],{i,nn/2},{j,i}]
%Y A378970 For primes we have A140119 or A376683, absolute value A376681 or A376684.
%Y A378970 For composites we have A377034, absolute value A377035.
%Y A378970 For squarefree numbers we have A377039, absolute value A377040.
%Y A378970 For nonsquarefree numbers we have A377047, absolute value A377048.
%Y A378970 For prime powers we have A377052, absolute value A377053.
%Y A378970 For partition numbers we have A377056, absolute value A378621.
%Y A378970 Row-sums of the triangular form of A378622. See also:
%Y A378970 - A175804 is the version for partitions.
%Y A378970 - A293467 gives the first column (up to sign).
%Y A378970 - A377285 gives position of first zero in each row.
%Y A378970 The unsigned version is A378971.
%Y A378970 A000009 counts strict integer partitions, differences A087897, A378972.
%Y A378970 A000041 counts integer partitions, differences A002865, A053445.
%Y A378970 Cf. A008284, A047966, A098859, A116608, A225486, A325242, A325244.
%K A378970 sign
%O A378970 0,4
%A A378970 _Gus Wiseman_, Dec 14 2024