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 A334463 a(n) is the sum of all parts of all partitions of n into consecutive parts that differ by 3. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 4 01:12 EDT 2024. Contains 374905 sequences. (Running on oeis4.)