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A145071
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Partial sums of A000051, starting at n=1.
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7
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3, 8, 17, 34, 67, 132, 261, 518, 1031, 2056, 4105, 8202, 16395, 32780, 65549, 131086, 262159, 524304, 1048593, 2097170, 4194323, 8388628, 16777237, 33554454, 67108887, 134217752, 268435481, 536870938, 1073741851, 2147483676
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OFFSET
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1,1
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COMMENTS
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The third number that is a sum of n positive n-th powers. - Alois P. Heinz, Aug 02 2020
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LINKS
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FORMULA
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a(1) = 3; a(n) = a(n-1) + 2^n + 1 for n > 1.
G.f.: x*(3-4*x)/((1-x)^2*(1-2*x)). - Colin Barker, Jan 11 2012
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EXAMPLE
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a(2) = a(1) + 2^2 + 1 = 3 + 4 + 1 = 8; a(3) = a(2) + 2^3 + 1 = 8 + 8 + 1 = 17.
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MATHEMATICA
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lst={}; s=0; Do[s+=2^n+1; AppendTo[lst, s], {n, 5!}]; lst
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PROG
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(ARIBAS) a:=0; for n:=1 to 30 do a:=a+2**n+1; write(a, ", "); end;
(Haskell)
a145071 n = 2 ^ (n + 1) + n - 2
a145071_list = scanl1 (+) $ tail a000051_list
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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