cp's OEIS Frontend

A024476 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = (Lucas numbers), t = A023533.

%I A024476 #7 Aug 01 2022 18:43:44
%S A024476 1,0,0,1,3,4,7,0,0,1,3,4,7,11,18,29,47,76,123,1,3,4,7,11,18,29,47,76,
%T A024476 123,199,322,521,843,1364,2208,3574,5782,9356,15138,18,29,47,76,123,
%U A024476 199,322,521,843,1364,2207,3571,5778,9349,15127,24476,39604,64082,103686,167768
%N A024476 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = (Lucas numbers), t = A023533.
%H A024476 G. C. Greubel, <a href="/A024476/b024476.txt">Table of n, a(n) for n = 1..5000</a>
%F A024476 a(n) = Sum_{k=1..floor((n+1)/2)} A000032(k) * A023533(n-k+1).
%t A024476 A023533[n_]:= A023533[n]= If[Binomial[Floor[Surd[6*n-1,3]]+2, 3]!= n,0,1];
%t A024476 A024476[n_]:= A024476[n]= Sum[LucasL[j]*A023533[n-j+1], {j, Floor[(n+1)/2]}];
%t A024476 Table[A024476[n], {n, 100}] (* _G. C. Greubel_, Aug 01 2022 *)
%o A024476 (Magma)
%o A024476 A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
%o A024476 [(&+[Lucas(k)*A023533(n+1-k): k in [1..Floor((n+1)/2)]]): n in [1..100]]; // _G. C. Greubel_, Aug 01 2022
%o A024476 (SageMath)
%o A024476 @CachedFunction
%o A024476 def A023533(n): return 0 if (binomial(floor((6*n-1)^(1/3)) +2, 3)!= n) else 1
%o A024476 def A024476(n): return sum(lucas_number2(j,1,-1)*A023533(n-j+1) for j in (1..((n+1)//2)))
%o A024476 [A024476(n) for n in (1..100)] # _G. C. Greubel_, Aug 01 2022
%Y A024476 Cf. A000032, A023533.
%K A024476 nonn
%O A024476 1,5
%A A024476 _Clark Kimberling_