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A129502 For n=2^k, a(n) = binomial(k + 2, 2), else 0.

%I A129502 #21 Oct 28 2023 04:04:44
%S A129502 1,3,0,6,0,0,0,10,0,0,0,0,0,0,0,15,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,21,0,
%T A129502 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,
%U A129502 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A129502 For n=2^k, a(n) = binomial(k + 2, 2), else 0.
%C A129502 Row sums of triangle A129501.
%H A129502 Andrew Howroyd, <a href="/A129502/b129502.txt">Table of n, a(n) for n = 1..1024</a>
%F A129502 From _Andrew Howroyd_, Aug 04 2018: (Start)
%F A129502 Multiplicative with a(2^e) = binomial(e + 2, 2), a(p^e) = 0 for odd prime p.
%F A129502 Dirichlet convolution of A104117 and A209229.
%F A129502 a(n) = Sum_{d|n} A104117(n/d) * A209229(d). (End)
%F A129502 Dirichlet g.f.: 1/(1 - 1/2^s)^3. - _Amiram Eldar_, Oct 28 2023
%e A129502 a(4) = 6 = sum of A129501 terms: (3 + 2 + 0 + 1).
%t A129502 Table[If[IntegerQ[Log2[n]],Binomial[Log2[n]+2,2],0],{n,100}] (* _Harvey P. Dale_, May 10 2022 *)
%o A129502 (PARI) a(n)={my(e=valuation(n, 2)); if(n==1<<e, binomial(2+e,2), 0)} \\ _Andrew Howroyd_, Aug 03 2018
%Y A129502 Row sums of A129501.
%Y A129502 Cf. A209229, A104117, A129360, A115361, A103994, A000217, A317673.
%K A129502 nonn,easy,mult
%O A129502 1,2
%A A129502 _Gary W. Adamson_, Apr 17 2007
%E A129502 Name changed and terms a(40) and beyond from _Andrew Howroyd_, Aug 03 2018