A334953 a(n) is the sum of all parts of all partitions of n into consecutive parts that differ by 6.

1, 2, 3, 4, 5, 6, 7, 16, 9, 20, 11, 24, 13, 28, 15, 32, 17, 36, 19, 40, 42, 44, 23, 72, 25, 52, 54, 56, 29, 90, 31, 64, 66, 68, 35, 108, 37, 76, 78, 120, 41, 126, 43, 132, 90, 92, 47, 192, 49, 100, 102, 156, 53, 162, 55, 168, 114, 116, 59, 240, 61, 124, 126, 192, 130, 198, 67, 204, 138, 210

Offset

1,2

Comments

The one-part partition n = n is included in the count.

Links

Table of n, a(n) for n=1..70.

Formula

a(n) = n*A334948(n).

Example

For n = 24 there are three partitions of 24 into consecutive parts that differ by 6, including 24 as a valid partition. They are [24], [15, 9] and [14, 8, 2]. The sum of all parts is [24] + [15 + 9] + [14 + 8 + 2] = 72, so a(24) = 72.

Crossrefs

Sequences of the same family where the parts differs by k are: A038040 (k=0), A245579 (k=1), A060872 (k=2), A334463 (k=3), A327262 (k=4), A334733 (k=5), this sequence (k=6).

Cf. A334946, A334947, A334948, A334949.

Sequence in context: A356194 A065640 A264974 * A308334 A161673 A368533

Adjacent sequences: A334950 A334951 A334952 * A334954 A334955 A334956

Keyword

nonn

Author

Omar E. Pol, May 27 2020

Status

approved