

A357487


Number of integer partitions of n with the same length as reversealternating sum.


11



1, 1, 0, 0, 0, 1, 0, 2, 0, 4, 0, 5, 0, 9, 0, 13, 0, 23, 0, 34, 0, 54, 0, 78, 0, 120, 0, 170, 0, 252, 0, 358, 0, 517, 0, 725, 0, 1030, 0, 1427, 0, 1992, 0, 2733, 0, 3759, 0, 5106, 0, 6946, 0, 9345, 0, 12577, 0, 16788, 0, 22384, 0, 29641, 0
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OFFSET

0,8


COMMENTS

A partition of n is a weakly decreasing sequence of positive integers summing to n.
The reversealternating sum of a sequence (y_1,...,y_k) is Sum_i (1)^i y_i.


LINKS



EXAMPLE

The a(1) = 1 through a(13) = 9 partitions:
1 . . . 311 . 322 . 333 . 443 . 553
421 432 542 652
531 641 751
51111 52211 52222
62111 53311
62221
63211
73111
7111111


MATHEMATICA

ats[y_]:=Sum[(1)^(i1)*y[[i]], {i, Length[y]}];
Table[Length[Select[IntegerPartitions[n], Length[#]==ats[Reverse[#]]&]], {n, 0, 30}]


CROSSREFS

These partitions are ranked by A357485.
A025047 counts alternating compositions.
A357136 counts compositions by alternating sum, full triangle A097805.


KEYWORD

nonn


AUTHOR



STATUS

approved



