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Sums of distinct nonzero terms of A003462: a(n) = Sum_{k>=0} A030308(n,k)*A003462(1+k).
2

%I #11 Mar 19 2017 19:39:36

%S 0,1,4,5,13,14,17,18,40,41,44,45,53,54,57,58,121,122,125,126,134,135,

%T 138,139,161,162,165,166,174,175,178,179,364,365,368,369,377,378,381,

%U 382,404,405,408,409,417,418,421,422,485,486,489,490,498,499,502,503,525,526,529,530,538,539,542,543,1093,1094,1097,1098,1106,1107,1110,1111

%N Sums of distinct nonzero terms of A003462: a(n) = Sum_{k>=0} A030308(n,k)*A003462(1+k).

%C Indexing starts from zero, with a(0) = 0.

%F a(n) = Sum_{i=0..A070939(n)} A030308(n,i)*A003462(1+i).

%F a(n) = A090880(A283477(n)).

%F Other identities. For all n >= 0:

%F a(2^n) = A003462(n+1).

%o (PARI)

%o A003462(n) = (3^n-1)/2;

%o A030308(n,k) = bittest(n,k);

%o A283483(n) = sum(i=0,(#binary(n)-1),A030308(n,i)*A003462(1+i));

%o (Scheme) (define (A283483 n) (A090880 (A283477 n)))

%Y Cf. A000244, A003462, A005187, A030308, A070939, A090880, A283477.

%K nonn

%O 0,3

%A _Antti Karttunen_, Mar 19 2017