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

Author

Omar E. Pol, May 27 2020

Keywords

• nonn

Comments

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

Examples

			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.

Formula

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