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A139701
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Binomial transform of [1, 100, 100, 100,...].
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7
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1, 101, 301, 701, 1501, 3101, 6301, 12701, 25501, 51101, 102301, 204701, 409501, 819101, 1638301, 3276701, 6553501, 13107101, 26214301, 52428701, 104857501, 209715101, 419430301, 838860701, 1677721501, 3355443101, 6710886301
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The binomial transform of [1, c, c, c,...] has the terms a(n)=1-c+c*2^(n-1) if the offset 1 is chosen. The o.g.f. of the a(n) is x{1+(c-2)x}/{(2x-1)(x-1)}. This applies to A139634 with c=10, to A139635 with c=11, to A139697 with c=12, to A139698 with c=25 and to A099003, A139700, A139701 accordingly. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 11 2008
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FORMULA
| A007318 * [1, 100, 100, 100,...].
a(n)=100*2^(n-1)-99. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 03 2008
a(n)=2*a(n-1)+99 (with a(1)=1) [From Vincenzo Librandi, Nov 24 2010]
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EXAMPLE
| a(3) = 301 = (1, 2, 1) dot (1, 100, 100) = (1 + 200 + 100).
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MAPLE
| a:=proc(n) options operator, arrow: 100*2^(n-1)-99 end proc: seq(a(n), n=1.. 30); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 03 2008
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CROSSREFS
| Cf. A139700, A099003, A139698, A139697, A139635, A139634.
Sequence in context: A142530 A033241 A140021 * A195294 A142578 A134971
Adjacent sequences: A139698 A139699 A139700 * A139702 A139703 A139704
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 29 2008
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 03 2008
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