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A023868 a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2) and t is A023533. 1

%I #12 Jul 22 2022 01:29:27

%S 1,0,0,1,2,3,4,0,0,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,11,12,13,

%T 14,15,17,19,21,23,25,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,

%U 25,27,29,31,33,35,37,39,41,43,45,47,49,15,16,17,18,19,20,21,22,23,24,25,26,27,28,30,32

%N a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2) and t is A023533.

%H G. C. Greubel, <a href="/A023868/b023868.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) = Sum_{j=1..floor((n+1)/2)} j * A023533(n-j+1).

%t A023533[n_]:= A023533[n]= If[Binomial[Floor[Surd[6*n-1,3]] +2, 3]!= n,0,1];

%t A023868[n_]:= A023868[n]= Sum[j*A023533[n-j+1], {j, Floor[(n+1)/2]}];

%t Table[A023868[n], {n, 100}] (* _G. C. Greubel_, Jul 21 2022 *)

%o (Magma)

%o A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;

%o [(&+[k*A023533(n+1-k): k in [1..Floor((n+1)/2)]]): n in [1..100]]; // _G. C. Greubel_, Jul 18 2022

%o (SageMath)

%o def A023533(n): return 0 if (binomial(floor((6*n-1)^(1/3)) +2, 3)!= n) else 1

%o def A023868(n): return sum(j*A023533(n-j+1) for j in (1..((n+1)//2)))

%o [A023868(n) for n in (1..100)] # _G. C. Greubel_, Jul 21 2022

%Y Cf. A023533.

%K nonn

%O 1,5

%A _Clark Kimberling_

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

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)