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A023866 a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2) and t is A000201 (lower Wythoff sequence). 1

%I

%S 1,3,10,14,32,43,77,93,147,169,248,283,393,437,582,644,829,903,1133,

%T 1219,1498,1608,1942,2067,2460,2601,3058,3230,3756,3946,4546,4772,

%U 5451,5699,6462,6732,7583,7895,8840,9177,10220,10604,11750,12162,13416,13856,15223,15717

%N a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2) and t is A000201 (lower Wythoff sequence).

%H G. C. Greubel, <a href="/A023866/b023866.txt">Table of n, a(n) for n = 1..1000</a>

%t Table[Sum[j*Floor[(n+1-j)*GoldenRatio], {j,1,Floor[(n+1)/2]}], {n, 1, 50}] (* _G. C. Greubel_, Jun 12 2019 *)

%o (PARI) {a(n) = sum(j=1, floor((n+1)/2), j*floor((n+1-j)*(1+sqrt(5))/2))}; \\ _G. C. Greubel_, Jun 12 2019

%o (MAGMA) [(&+[j*Floor((n+1-j)*(1+Sqrt(5))/2): j in [1..Floor((n+1)/2)]]): n in [1..50]]; // _G. C. Greubel_, Jun 12 2019

%o (Sage) [sum(j*floor((n+1-j)*golden_ratio) for j in (1..floor((n+1)/2))) for n in (1..50)] # _G. C. Greubel_, Jun 12 2019

%K nonn

%O 1,2

%A _Clark Kimberling_

%E Title simplified by _Sean A. Irvine_, Jun 12 2019

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Last modified September 24 09:44 EDT 2021. Contains 347630 sequences. (Running on oeis4.)