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 A327262 #43 Nov 26 2023 11:30:21
%S A327262 1,2,3,4,5,12,7,16,9,20,11,24,13,28,30,32,17,54,19,40,42,44,23,72,25,
%T A327262 52,54,84,29,90,31,96,66,68,35,144,37,76,78,120,41,126,43,132,135,92,
%U A327262 47,192,49,150,102,156,53,162,110,168,114,116,59,300,61,124,126,192,130,264,67,204,138,210
%N A327262 a(n) is the sum of all parts of all partitions of n into consecutive parts that differ by 4.
%C A327262 The one-part partition n = n is included in the count.
%F A327262 a(n) = n*A334461(n).
%e A327262 For n = 28 there are three partitions of 28 into consecutive parts that differ by 4, including 28 as a valid partition. They are [28], [16, 12] and [13, 9, 5, 1]. The sum of the parts is [28] + [16 + 12] + [13 + 9 + 5 + 1] = 84, so a(28) = 84.
%t A327262 pn4[n_]:=Total[Flatten[Select[IntegerPartitions[n],Union[Abs[Differences[#]]]=={4}&]]]+n; Array[pn4,70] (* _Harvey P. Dale_, Nov 26 2023 *)
%Y A327262 Cf. A334460, A334461.
%Y A327262 Sequences of the same family where the parts differs by k are: A038040 (k=0), A245579 (k=1), A060872 (k=2), A334463 (k=3), this sequence (k=4), A334733 (k=5).
%K A327262 nonn
%O A327262 1,2
%A A327262 _Omar E. Pol_, Apr 30 2020