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a(n) = sum_{k >= 0, k even} binomial(wt(n+k),k+1), where wt() = A000120().
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%I #2 Mar 30 2012 16:51:03

%S 1,2,1,2,2,4,1,2,2,4,2,5,4,7,1,2,2,4,2,5,4,7,2,5,4,8,5,12,7,11,1,2,2,

%T 4,2,5,4,7,2,5,4,8,5,12,7,11,2,5,4,8,5,12,7,12,5,12,8,17,12,26,11,16,

%U 1,2,2,4,2,5,4,7,2,5,4,8,5,12,7,11,2,5,4,8,5,12,7,12,5,12,8,17,12,26,11,16

%N a(n) = sum_{k >= 0, k even} binomial(wt(n+k),k+1), where wt() = A000120().

%p wt := proc(n) local w,m,i; w := 0; m := n; while m > 0 do i := m mod 2; w := w+i; m := (m-i)/2; od; w; end:

%p f:=proc(n) local t1,k; global wt; t1:=0; for k from 0 to 20 do if k mod 2 = 0 then t1:=t1+binomial(wt(n+k),k); fi; od; t1; end;

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jun 01 2009