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A139701
Binomial transform of [1, 100, 100, 100, ...].
7
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, 13421772701, 26843545501
OFFSET
1,2
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 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, May 11 2008
FORMULA
A007318 * [1, 100, 100, 100, ...].
a(n) = 100*2^(n-1)-99. - Emeric Deutsch, May 03 2008
a(n) = 2*a(n-1)+99 for n > 1. [Vincenzo Librandi, Nov 24 2010]
a(n) = 3*a(n-1) - 2*a(n-2) for n > 2. G.f.: x*(98*x+1) / ((x-1)*(2*x-1)). - Colin Barker, Mar 11 2014
EXAMPLE
a(3) = 301 = (1, 2, 1) dot (1, 100, 100) = (1 + 200 + 100).
MAPLE
a:=proc(n) options operator, arrow: 100*2^(n-1)-99 end proc: seq(a(n), n=1.. 30); # Emeric Deutsch, May 03 2008
MATHEMATICA
100*2^(Range[30] - 1) - 99 (* Wesley Ivan Hurt, Aug 16 2016 *)
LinearRecurrence[{3, -2}, {1, 101}, 40] (* Vincenzo Librandi, Aug 17 2016 *)
PROG
(PARI) Vec(x*(98*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 11 2014
(Magma) [100*2^(n-1)-99 : n in [1..30]]; // Wesley Ivan Hurt, Aug 16 2016
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Apr 29 2008
EXTENSIONS
More terms from Emeric Deutsch, May 03 2008
More terms from Colin Barker, Mar 11 2014
STATUS
approved