cp's OEIS Frontend

A378972 Second differences of the strict partition numbers A000009.

%I A378972 #5 Dec 14 2024 20:29:53
%S A378972 0,1,-1,1,0,0,0,1,0,0,1,0,1,1,0,1,2,0,2,2,1,2,3,2,3,4,3,4,6,4,6,8,6,9,
%T A378972 10,9,12,14,13,16,19,18,22,26,24,30,34,34,40,45,46,53,60,62,70,79,82,
%U A378972 93,104,108,122,136,142,160,176,186,208,228,243,268
%N A378972 Second differences of the strict partition numbers A000009.
%e A378972 The strict partition numbers begin (A000009):
%e A378972   1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, ...
%e A378972 with differences (A087897 without first term):
%e A378972   0, 0, 1, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 8, 8, 10, 12, ...
%e A378972 with differences (a(n)):
%e A378972   0, 1, -1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 2, 0, 2, 2, 1, 2, ...
%t A378972 Differences[Table[PartitionsQ[n],{n,0,100}],2]
%Y A378972 For primes we have A036263.
%Y A378972 The version for partitions is A053445.
%Y A378972 For composites we have A073445.
%Y A378972 For squarefree numbers we have A376590.
%Y A378972 For nonsquarefree numbers we have A376593.
%Y A378972 For powers of primes (inclusive) we have A376596.
%Y A378972 For non powers of primes (inclusive) we have A376599.
%Y A378972 Second row of A378622. See also:
%Y A378972 - A293467 gives first column (up to sign).
%Y A378972 - A377285 gives position of first zero in each row.
%Y A378972 - A378970 gives row-sums.
%Y A378972 - A378971 gives absolute value row-sums.
%Y A378972 A000009 counts strict integer partitions, differences A087897, A378972.
%Y A378972 A000041 counts integer partitions, differences A002865, A053445.
%Y A378972 Cf. A047966, A098859, A225486, A325244, A325282.
%Y A378972 Cf. A008284, A116608, A225485, A325242, A325268.
%K A378972 sign
%O A378972 0,17
%A A378972 _Gus Wiseman_, Dec 14 2024