A241761 - OEIS

A241761

Number of partitions p = [x(1), ..., x(k)], where x(1) >= x(2) >= ... >= x(k), of n such that min(x(i) - x(i-1)) is not a part of p.

1, 1, 2, 2, 5, 7, 9, 14, 20, 28, 39, 54, 71, 96, 127, 167, 220, 286, 368, 473, 604, 766, 970, 1219, 1528, 1907, 2373, 2939, 3634, 4472, 5489, 6715, 8198, 9972, 12109, 14658, 17711, 21340, 25669, 30796, 36890, 44082, 52594, 62613, 74435, 88303, 104613, 123698

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OFFSET

0,3

COMMENTS

The partition {n} is included in the count.

LINKS

Table of n, a(n) for n=0..47.

FORMULA

a(n) + A241760(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 6 partitions: 6, 51, 411, 33, 3111, 222, 2211, 21111, 111111.

MATHEMATICA