A334463 a(n) is the sum of all parts of all partitions of n into consecutive parts that differ by 3.

1, 2, 3, 4, 10, 6, 14, 8, 18, 10, 22, 24, 26, 14, 45, 16, 34, 36, 38, 20, 63, 44, 46, 48, 50, 52, 81, 28, 58, 90, 62, 32, 99, 68, 105, 72, 74, 76, 117, 80, 82, 126, 86, 44, 180, 92, 94, 96, 98, 150, 204, 52, 106, 162, 165, 56, 228, 116, 118, 180, 122, 124, 252, 64, 195, 198, 134, 68, 276, 280, 142, 144

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..72.

Formula

a(n) = n*A117277(n).

Example

For n = 21 there are three partitions of 21 into consecutive parts that differ by 3, including 21 as a valid partition. They are [21], [12, 9] and [10, 7, 4]. The sum of the parts is [21] + [12 + 9] + [10 + 7 + 4] = 63, the same as 3*21 = 63, since there are three of these partitions of 21, so a(21) = 63.

Crossrefs

Cf. A038040, A245579, A330887, A330888, A330889.

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

Sequence in context: A353959 A111619 A241083 * A143178 A084190 A203070

Adjacent sequences: A334460 A334461 A334462 * A334464 A334465 A334466

Keyword

nonn

Author

Omar E. Pol, May 05 2020

Status

approved