This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A334463 #23 Nov 21 2020 11:27:38 %S A334463 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, %T A334463 52,81,28,58,90,62,32,99,68,105,72,74,76,117,80,82,126,86,44,180,92, %U A334463 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 %N A334463 a(n) is the sum of all parts of all partitions of n into consecutive parts that differ by 3. %C A334463 The one-part partition n = n is included in the count. %F A334463 a(n) = n*A117277(n). %e A334463 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. %Y A334463 Cf. A038040, A245579, A330887, A330888, A330889. %Y A334463 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). %K A334463 nonn %O A334463 1,2 %A A334463 _Omar E. Pol_, May 05 2020