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A045618
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Partial sums of A000337(n+4), n >= 0.
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17
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1, 6, 23, 72, 201, 522, 1291, 3084, 7181, 16398, 36879, 81936, 180241, 393234, 851987, 1835028, 3932181, 8388630, 17825815, 37748760, 79691801, 167772186, 352321563, 738197532, 1543503901, 3221225502, 6710886431, 13958643744
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Convolution of A000225(n+1), n >= 0, (partial sums of powers of 2).
Sum of diameters of all nonempty subsets of {1, 2, ..., n+2}. [Charles R Greathouse IV, Nov 21 2011]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (6,-13,12,-4).
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FORMULA
| a(n) = n+5+(n-1)*2^(n+2); G.f.: 1/((1-2*x)*(1-x))^2.
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MATHEMATICA
| Table[Sum[(-1)^(n - k) k (-1)^(n - k) Binomial[n + 2, k + 2], {k, 0, n}], {n, 1, 28}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2009]
Rest[Accumulate[LinearRecurrence[{5, -8, 4}, {0, 1, 5}, 40]]] (* From Harvey P. Dale, Dec 19 2011 *)
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PROG
| (PARI) a(n)=(n-1)<<(n+2)+n+5 \\ Charles R Greathouse IV, Nov 21 2011
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CROSSREFS
| Sequence in context: A009017 A119712 A005745 * A038737 A038797 A136530
Adjacent sequences: A045615 A045616 A045617 * A045619 A045620 A045621
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KEYWORD
| easy,nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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