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A139635
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Binomial transform of [1, 11, 11, 11,...].
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7
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1, 12, 34, 78, 166, 342, 694, 1398, 2806, 5622, 11254, 22518, 45046, 90102, 180214, 360438, 720886, 1441782, 2883574, 5767158, 11534326, 23068662, 46137334, 92274678, 184549366
(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, 11, 11, 11,...].
a(n)=11*2^(n-1)-10. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 03 2008
a(n)=2*a(n-1)+10 (with a(1)=1) [From Vincenzo Librandi, Nov 24 2010]
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EXAMPLE
| a(4) = 78 = (1, 3, 3, 1) dot (1, 11, 11, 11) = (1 + 33 + 33 + 11).
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MAPLE
| seq(11*2^(n-1)-10, n=1.. 25); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 03 2008
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MATHEMATICA
| a=1; lst={a}; k=11; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 17 2008]
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CROSSREFS
| Cf. A139634.
Sequence in context: A113748 A069125 A142245 * A124705 A126366 A199114
Adjacent sequences: A139632 A139633 A139634 * A139636 A139637 A139638
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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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