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A005126
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2^n + n + 1.
(Formerly M1061)
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11
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2, 4, 7, 12, 21, 38, 71, 136, 265, 522, 1035, 2060, 4109, 8206, 16399, 32784, 65553, 131090, 262163, 524308, 1048597, 2097174, 4194327, 8388632, 16777241, 33554458, 67108891, 134217756, 268435485, 536870942, 1073741855, 2147483680, 4294967329, 8589934626
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Binomial transform of (1, 1, 1, 0, 1, 0, 1, 0, 1,...). - Gary W. Adamson, Jul 20 2007
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..2000
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 921
Index to sequences with linear recurrences with constant coefficients, signature (4,-5,2).
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FORMULA
| G.f.: (2-4*x+x^2)/((1-2*x)*(1-x)^2). [From S. Plouffe]
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MAPLE
| A005126:=-(2-4*z+z**2)/(2*z-1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
g:=z/(1-2*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)+n, n=1..34); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 11 2009]
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MATHEMATICA
| s=2; lst={s}; Do[s+=(s-n); AppendTo[lst, Abs[s]], {n, 0, 5!}]; lst [From Vladimir Orlovsky, Oct 10 2008]
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PROG
| (MAGMA) [2^n+n+1: n in [0..40]]; // Vincenzo Librandi, Oct 22 2011
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CROSSREFS
| Essentially the same as row sums of A128715.
Cf. A194455.
Sequence in context: A054161 A023433 A190168 * A054151 A018176 A135460
Adjacent sequences: A005123 A005124 A005125 * A005127 A005128 A005129
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KEYWORD
| nonn,easy
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AUTHOR
| C. L. Mallows (colinm(AT)research.avayalabs.com)
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EXTENSIONS
| More terms from N. J. A. Sloane (njas(AT)research.att.com), Sep 28 2007
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