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 A376468 #19 Jun 16 2025 17:25:46
%S A376468 1,2,6,3,7,11,4,8,12,16,5,9,13,17,21,10,14,18,22,26,30,15,19,23,27,31,
%T A376468 35,39,20,24,28,32,36,40,44,48,25,29,33,37,41,45,49,53,57,34,38,42,46,
%U A376468 50,54,58,62,66,70,43,47,51,55,59,63,67,71,75,79,83,52,56,60,64,68,72,76,80,84,88,92,96
%N A376468 Triangle T read by rows: T(n, k) = (n^2 - 2*n + 3 - (-1)^n + n^2 mod 8) / 2 + 4*k.
%C A376468 This triangle seen as a sequence yields a permutation of the natural numbers. For similar triangles see A000027 (seen as a triangle), A074147, and A367844 (row reversed).
%H A376468 Paolo Xausa, <a href="/A376468/b376468.txt">Table of n, a(n) for n = 0..11475</a> (rows 0..150 of triangle, flattened).
%F A376468 T(n, k) = T(n, k-1) + 4.
%F A376468 T(n+4, 0) = T(n, n) + 4 for n > 3.
%F A376468 T(2*n, n) = 2 * (n^2 + n + 1) - (-1)^n = A001844(n) + 1 - (-1)^n.
%e A376468 Triangle T(n, k) for 0 <= k <= n starts:
%e A376468 n \k : 0 1 2 3 4 5 6 7 8 9 10 11
%e A376468 ======================================================
%e A376468 0 : 1
%e A376468 1 : 2 6
%e A376468 2 : 3 7 11
%e A376468 3 : 4 8 12 16
%e A376468 4 : 5 9 13 17 21
%e A376468 5 : 10 14 18 22 26 30
%e A376468 6 : 15 19 23 27 31 35 39
%e A376468 7 : 20 24 28 32 36 40 44 48
%e A376468 8 : 25 29 33 37 41 45 49 53 57
%e A376468 9 : 34 38 42 46 50 54 58 62 66 70
%e A376468 10 : 43 47 51 55 59 63 67 71 75 79 83
%e A376468 11 : 52 56 60 64 68 72 76 80 84 88 92 96
%e A376468 etc.
%t A376468 Table[Range[#, #+n*4, 4] & [(Mod[n^2, 8] + n*(n-2) - (-1)^n + 3)/2], {n, 0, 15}] (* _Paolo Xausa_, Nov 13 2024 *)
%o A376468 (PARI) T(n,k)=(n^2-2*n+3-(-1)^n+n^2%8)/2+4*k
%o A376468 (Python)
%o A376468 from math import comb, isqrt
%o A376468 def A376468(n): return ((a:=(m:=isqrt(k:=n+1<<1))-(k<=m*(m+1)))*(a-2)+3+(1 if a&1 else -1)+(a**2&7)>>1)+(n-comb(a+1,2)<<2) # _Chai Wah Wu_, Nov 12 2024
%Y A376468 Cf. A001844
%K A376468 nonn,easy,tabl
%O A376468 0,2
%A A376468 _Werner Schulte_, Sep 23 2024