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%I #15 Nov 22 2020 12:19:08
%S 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,
%T 52,54,56,29,90,31,64,66,68,35,108,37,76,78,120,41,126,43,132,90,92,
%U 47,192,49,100,102,156,53,162,55,168,114,116,59,240,61,124,126,192,130,198,67,204,138,210
%N a(n) is the sum of all parts of all partitions of n into consecutive parts that differ by 6.
%C The one-part partition n = n is included in the count.
%F a(n) = n*A334948(n).
%e 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.
%Y 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).
%Y Cf. A334946, A334947, A334948, A334949.
%K nonn
%O 1,2
%A _Omar E. Pol_, May 27 2020