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 A339572 #22 Jun 24 2025 11:47:21
%S A339572 0,0,1,2,2,3,4,6,7,10,12,17,20,28,33,46,54,75,88,122,143,198,232,321,
%T A339572 376,520,609,842,986,1363,1596,2206,2583,3570,4180,5777,6764,9348,
%U A339572 10945,15126,17710,24475,28656,39602,46367,64078,75024,103681,121392,167760,196417,271442
%N A339572 If n even, a(n) = A000071(n/2+1); if n odd, a(n) = A001610((n-1)/2).
%C A339572 Sequences A000071 and A001610 look like long-lost cousins, and this entry smoothly interleaves them. Differences between successive terms are Fibonacci numbers.
%H A339572 Stefano Spezia, <a href="/A339572/b339572.txt">Table of n, a(n) for n = 0..1000</a>
%F A339572 a(n) = Fibonacci(k+2) + Fibonacci(k)*(n mod 2) - 1, where k = floor(n/2). - _Wesley Ivan Hurt_, Dec 09 2020
%t A339572 Block[{b = {0, 2}, a = {}}, Do[If[EvenQ[i], AppendTo[b, Total@ b[[-2 ;; -1]] + 1 ]; AppendTo[a, Fibonacci[i/2 + 1] - 1], AppendTo[a, b[[(i - 1)/2]]]], {i, 2, 53}]; a] (* _Michael De Vlieger_, Dec 09 2020 *)
%t A339572 Table[With[{k=Floor[n/2]},Fibonacci[k+2]+Fibonacci[k]Mod[n,2]-1],{n,0,60}] (* _Harvey P. Dale_, Jun 24 2025 *)
%Y A339572 Cf. A000045, A000071, A001610.
%Y A339572 The first differences are essentially A053602.
%K A339572 nonn
%O A339572 0,4
%A A339572 _N. J. A. Sloane_, Dec 09 2020