cp's OEIS Frontend

A024322 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 = (F(2), F(3), ...).

%I A024322 #8 Jan 21 2022 07:49:54
%S A024322 0,0,2,3,5,8,13,21,42,68,110,178,288,466,754,1220,2029,3283,5312,8595,
%T A024322 13907,22502,36409,58911,95320,154231,250161,404769,654930,1059699,
%U A024322 1714629,2774328,4488957,7263285
%N A024322 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 = (F(2), F(3), ...).
%H A024322 G. C. Greubel, <a href="/A024322/b024322.txt">Table of n, a(n) for n = 1..1000</a>
%F A024322 From _G. C. Greubel_, Jan 20 2022: (Start)
%F A024322 a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*A000045(n-j+1).
%F A024322 a(n) = Sum_{j=1..floor((n+1)/2)} A010054(j+1)*A000045(n-j+2). (End)
%t A024322 A010054[n_]:= SquaresR[1, 8n+1]/2;
%t A024322 a[n_]:= Sum[A010054[j+1]*Fibonacci[n-j+2], {j, Floor[(n+1)/2]}];
%t A024322 Table[a[n], {n, 40}] (* _G. C. Greubel_, Jan 20 2022 *)
%o A024322 (Magma)
%o A024322 A023531:= func< n | IsIntegral( (Sqrt(8*n+9) - 3)/2 ) select 1 else 0 >;
%o A024322 [ (&+[A023531(j)*Fibonacci(n-j+2): j in [1..Floor((n+1)/2)]]) : n in [1..40]]; // _G. C. Greubel_, Jan 20 2022
%o A024322 (Sage)
%o A024322 def A023531(n):
%o A024322     if ((sqrt(8*n+9) -3)/2).is_integer(): return 1
%o A024322     else: return 0
%o A024322 [sum( A023531(j)*fibonacci(n-j+2) for j in (1..floor((n+1)/2)) ) for n in (1..40)] # _G. C. Greubel_, Jan 20 2022
%Y A024322 Cf. A024312, A024313, A024314, A024315, A024316, A024317, A024318, A024319, A024320, A024321, A024323, A024324, A024325, A024326, A024327.
%Y A024322 Cf. A000045, A010054, A023531.
%K A024322 nonn
%O A024322 1,3
%A A024322 _Clark Kimberling_