cp's OEIS Frontend

A378971 Antidiagonal-sums of absolute value of the array A378622(n,k) = n-th term of k-th differences of strict partition numbers (A000009).

%I A378971 #6 Dec 14 2024 20:29:58
%S A378971 1,1,1,5,8,18,30,47,70,110,177,309,574,1063,1892,3107,4598,6166,8737,
%T A378971 20603,62457,149132,314116,614093,1155968,2176048,4244322,8753864,
%U A378971 19006756,42472117,95235017,210396059,453414950,949510166,1931941261,3826650257,7400745917
%N A378971 Antidiagonal-sums of absolute value of the array A378622(n,k) = n-th term of k-th differences of strict partition numbers (A000009).
%e A378971 Antidiagonal 4 of A378622 is (2, 0, -1, -2, -3), so a(4) = 8.
%t A378971 nn=30;
%t A378971 t=Table[Take[Differences[PartitionsQ/@Range[0,2nn],k],nn],{k,0,nn}];
%t A378971 Total/@Abs/@Table[t[[j,i-j+1]],{i,nn/2},{j,i}]
%Y A378971 For primes we have A376681 or A376684, signed version A140119 or A376683.
%Y A378971 For composites we have A377035, signed version A377034.
%Y A378971 For squarefree numbers we have A377040, signed version A377039.
%Y A378971 For nonsquarefree numbers we have A377048, signed version A377049.
%Y A378971 For prime powers we have A377053, signed version A377052.
%Y A378971 For partition numbers we have A378621, signed version A377056.
%Y A378971 Row-sums of the triangular form of A378622. See also:
%Y A378971 - A175804 is the version for partitions.
%Y A378971 - A293467 gives the first column (up to sign).
%Y A378971 - A377285 gives position of first zero in each row.
%Y A378971 The signed version is A378970.
%Y A378971 A000009 counts strict integer partitions, differences A087897, A378972.
%Y A378971 A000041 counts integer partitions, differences A002865, A053445.
%Y A378971 Cf. A008284, A047966, A098859, A116608, A225486, A325242, A325244, A325245, A325268.
%K A378971 nonn
%O A378971 0,4
%A A378971 _Gus Wiseman_, Dec 14 2024