A342515 - OEIS

A342515

Number of strict partitions of n with constant (equal) first-quotients.

1, 1, 1, 2, 2, 3, 3, 5, 4, 5, 5, 6, 6, 8, 8, 9, 8, 9, 9, 11, 10, 13, 11, 12, 12, 13, 14, 14, 15, 15, 16, 18, 16, 17, 17, 19, 18, 20, 20, 22, 21, 21, 23, 23, 22, 24, 23, 24, 24, 27, 25, 26, 27, 27, 27, 28, 29, 31, 29, 30, 31, 32, 33, 35, 32, 35, 33, 35, 34, 35

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OFFSET

0,4

COMMENTS

Also the number of reversed strict partitions of n with constant (equal) first-quotients.

The first quotients of a sequence are defined as if the sequence were an increasing divisor chain, so for example the quotients of (6,3,1) are (1/2,1/3).

LINKS

Table of n, a(n) for n=0..69.

Wikipedia, Arithmetic progression

Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

Gus Wiseman, Sequences counting and ranking partitions and compositions by their differences and quotients.

EXAMPLE

The a(1) = 1 through a(15) = 9 partitions (A..F = 10..15):

1 2 3 4 5 6 7 8 9 A B C D E F

21 31 32 42 43 53 54 64 65 75 76 86 87

41 51 52 62 63 73 74 84 85 95 96

61 71 72 82 83 93 94 A4 A5

421 81 91 92 A2 A3 B3 B4