A241736 - OEIS

A241736

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

1, 1, 2, 2, 4, 5, 7, 10, 15, 20, 27, 37, 49, 67, 89, 115, 150, 196, 248, 322, 409, 519, 653, 824, 1025, 1282, 1587, 1967, 2420, 2986, 3645, 4469, 5436, 6617, 8009, 9705, 11684, 14093, 16906, 20290, 24247, 28992, 34508, 41103, 48773, 57865, 68438, 80941

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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) + A241735(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 7 partitions: 6, 51, 411, 33, 3111, 222, 11111.

MATHEMATICA