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A145071
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Partial sums of A000051, starting at n=1.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
| a(1) = 3; a(n) = a(n-1) + 2^n + 1 for n > 1.
a(n) = 2^(n+1) + n - 2. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jul 06 2009]
G.f.: x*(3-4*x)/((1-x)^2*(1-2*x)). [Colin Barker, Jan 11 2012]
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EXAMPLE
| 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
| lst={}; s=0; Do[s+=2^n+1; AppendTo[lst, s], {n, 5!}]; lst
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PROG
| (ARIBAS) a:=0; for n:=1 to 30 do a:=a+2**n+1; write(a, ", "); end;
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CROSSREFS
| Cf. A000051 (2^n + 1), A000225 (2^n - 1), A000295 (Eulerian numbers).
Sequence in context: A029859 A163312 A131253 * A182734 A182616 A159217
Adjacent sequences: A145068 A145069 A145070 * A145072 A145073 A145074
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KEYWORD
| nonn
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AUTHOR
| Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 30 2008
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EXTENSIONS
| Edited. - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 14 2008
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