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If n even, a(n) = A000071(n/2+1); if n odd, a(n) = A001610((n-1)/2).
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%I #20 Dec 10 2020 04:14:19

%S 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 376,520,609,842,986,1363,1596,2206,2583,3570,4180,5777,6764,9348,

%U 10945,15126,17710,24475,28656,39602,46367,64078,75024,103681,121392,167760,196417,271442

%N If n even, a(n) = A000071(n/2+1); if n odd, a(n) = A001610((n-1)/2).

%C Sequences A000071 and A001610 look like long-lost cousins, and this entry smoothly interleaves them. Differences between successive terms are Fibonacci numbers.

%H Stefano Spezia, <a href="/A339572/b339572.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = Fibonacci(k+2) + Fibonacci(k)*(n mod 2) - 1, where k = floor(n/2). - _Wesley Ivan Hurt_, Dec 09 2020

%t 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 *)

%Y Cf. A000045, A000071, A001610.

%Y The first differences are essentially A053602.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Dec 09 2020