A334733 a(n) is the sum of all parts of all partitions of n into consecutive parts that differ by 5.

1, 2, 3, 4, 5, 6, 14, 8, 18, 10, 22, 12, 26, 14, 30, 16, 34, 36, 38, 20, 63, 22, 46, 48, 50, 26, 81, 28, 58, 60, 62, 32, 99, 68, 70, 72, 74, 76, 117, 40, 82, 126, 86, 44, 135, 92, 94, 96, 98, 100, 153, 52, 106, 162, 165, 56, 171, 116, 118, 180, 122, 124, 189, 64, 195, 198, 134, 68, 207, 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*A334541(n).

Example

For n = 27 there are three partitions of 27 into consecutive parts that differ by 5, including 27 as a valid partition. They are [27], [16, 11] and [14, 9, 4]. The sum of all parts is [27] + [16 + 11] + [14 + 9 + 4] = 81, so a(27) = 81.

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), this sequence (k=5).

Cf. A334465, A334541.

Sequence in context: A065638 A364224 A204896 * A039016 A249102 A250047

Adjacent sequences: A334730 A334731 A334732 * A334734 A334735 A334736

Keyword

nonn

Author

Omar E. Pol, May 09 2020

Status

approved