cp's OEIS Frontend

A023867 a(n) = 1*t(n) + 2*t(n-1) + ...+ k*t(n+1-k), where k=floor((n+1)/2) and t is A001950 (upper Wythoff sequence).

%I A023867 #12 Sep 08 2022 08:44:47
%S A023867 2,5,17,24,54,71,127,153,242,279,409,465,645,717,954,1052,1354,1473,
%T A023867 1848,1989,2444,2620,3164,3367,4007,4239,4983,5260,6116,6426,7402,
%U A023867 7764,8868,9269,10509,10950,12333,12835,14370,14917,16611,17226,19087,19752,21788,22504
%N A023867 a(n) = 1*t(n) + 2*t(n-1) + ...+ k*t(n+1-k), where k=floor((n+1)/2) and t is A001950 (upper Wythoff sequence).
%H A023867 G. C. Greubel, <a href="/A023867/b023867.txt">Table of n, a(n) for n = 1..1000</a>
%t A023867 f[n_]:= n +Floor[n*GoldenRatio]; Table[Sum[j*f[n+1-j], {j,1,Floor[(n + 1)/2]}], {n, 1, 50}] (* _G. C. Greubel_, Jun 12 2019 *)
%o A023867 (PARI) f(n) = n + floor(n*(1+sqrt(5))/2);
%o A023867 a(n) = sum(j=1, floor((n+1)/2), j*f(n+1-j)); \\ _G. C. Greubel_, Jun 12 2019
%o A023867 (Magma) f:= func< n | n + Floor(n*(1+Sqrt(5))/2) >;
%o A023867 [(&+[j*f(n+1-j): j in [1..Floor((n+1)/2)]]): n in [1..50]]; // _G. C. Greubel_, Jun 12 2019
%o A023867 (Sage)
%o A023867 def f(n): return n + floor(n*golden_ratio)
%o A023867 [sum(j*f(n+1-j) for j in (1..floor((n+1)/2))) for n in (1..50)] # _G. C. Greubel_, Jun 12 2019
%K A023867 nonn
%O A023867 1,1
%A A023867 _Clark Kimberling_
%E A023867 Title simplified by _Sean A. Irvine_, Jun 12 2019