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A024318 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (Fibonacci numbers).

%I A024318 #16 Feb 04 2022 08:13:48
%S A024318 0,0,1,2,3,5,8,13,26,42,68,110,178,288,466,754,1254,2029,3283,5312,
%T A024318 8595,13907,22502,36409,58911,95320,154608,250161,404769,654930,
%U A024318 1059699,1714629,2774328,4488957,7263285
%N A024318 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (Fibonacci numbers).
%H A024318 G. C. Greubel, <a href="/A024318/b024318.txt">Table of n, a(n) for n = 1..1000</a>
%F A024318 a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*Fibonacci(n-j+1). - _G. C. Greubel_, Jan 19 2022
%t A024318 Table[t=0; m=3; p=BitShiftRight[n]; n--; While[n>p, t += Fibonacci[n+1]; n -= m++]; t, {n, 120}] (* _G. C. Greubel_, Jan 19 2022 *)
%o A024318 (Magma)
%o A024318 b:= func< n,j | IsIntegral((Sqrt(8*j+9) -3)/2) select Fibonacci(n-j+1) else 0 >;
%o A024318 A024318:= func< n | (&+[b(n,j): j in [1..Floor((n+1)/2)]]) >;
%o A024318 [A024318(n) : n in [1..80]]; // _G. C. Greubel_, Jan 19 2022
%o A024318 (Sage)
%o A024318 def b(n,j): return fibonacci(n-j+1) if ((sqrt(8*j+9) -3)/2).is_integer() else 0
%o A024318 def A024318(n): return sum( b(n,j) for j in (1..floor((n+1)/2)) )
%o A024318 [A024318(n) for n in (1..120)] # _G. C. Greubel_, Jan 19 2022
%Y A024318 Cf. A024312, A024313, A024314, A024315, A024316, A024317, A024319, A024320, A024321, A024322, A024323, A024324, A024325, A024326, A024327.
%Y A024318 Cf. A000045, A023531.
%K A024318 nonn
%O A024318 1,4
%A A024318 _Clark Kimberling_