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A130252
Partial sums of A130250.
9
0, 1, 4, 7, 11, 15, 20, 25, 30, 35, 40, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 267, 275, 283, 291, 299, 307, 315, 323, 331, 339, 347, 355, 363, 371
OFFSET
0,3
COMMENTS
If the initial zero is omitted, partial sums of A130253.
LINKS
FORMULA
a(n) = Sum_{k=0..n} A130250(k).
a(n) = n*ceiling(log_2(3n-1)) - (1/2)*( A001045(ceiling(log_2(3n-1)) +1) - 1 ).
G.f.: (1/(1-x)^2)*Sum_{k>=0} x^A001045(k).
MATHEMATICA
A001045[n_]:= (2^n - (-1)^n)/3;
A130252[n_]:= If[n==0, 0, (2*n*Ceiling[Log[2, 3*n-1]] - A001045[Ceiling[Log[2, 3*n-1]]+1] +1)/2];
Table[A130252[n], {n, 0, 70}] (* G. C. Greubel, Mar 18 2023 *)
PROG
(Magma)
A001045:= func< n | (2^n - (-1)^n)/3 >;
A130252:= func< n | n eq 0 select 0 else (2*n*Ceiling(Log(2, 3*n-1)) - A001045(Ceiling(Log(2, 3*n-1)) +1) +1)/2 >;
[A130252(n): n in [0..70]]; // G. C. Greubel, Mar 18 2023
(SageMath)
def A001045(n): return (2^n - (-1)^n)/3
def A130252(n): return 0 if (n==0) else (2*n*ceil(log(3*n-1, 2)) - A001045(ceil(log(3*n-1, 2)) +1) +1)/2
[A130252(n) for n in range(71)] # G. C. Greubel, Mar 18 2023
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, May 20 2007
STATUS
approved