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A139697
Binomial transform of [1, 12, 12, 12, ...].
9
1, 13, 37, 85, 181, 373, 757, 1525, 3061, 6133, 12277, 24565, 49141, 98293, 196597, 393205, 786421, 1572853, 3145717, 6291445, 12582901, 25165813, 50331637, 100663285, 201326581, 402653173, 805306357, 1610612725, 3221225461, 6442450933, 12884901877
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 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, May 11 2008
FORMULA
A007318 * [1, 12, 12, 12, ...].
a(n) = 12*2^(n-1) - 11. - Emeric Deutsch, May 05 2008
a(n) = 2*a(n-1) + 11 (with a(1)=1). - Vincenzo Librandi, Nov 24 2010
From Colin Barker, Oct 10 2013: (Start)
a(n) = 3*2^(n+1) - 11.
a(n) = 3*a(n-1) - 2*a(n-2).
G.f.: x*(10*x+1) / ((x-1)*(2*x-1)). (End)
EXAMPLE
a(4) = 85 = (1, 3, 3, 1) dot (1, 12, 12, 12) = (1 + 36 + 36 + 12).
MAPLE
seq(12*2^(n-1)-11, n=1..25); # Emeric Deutsch, May 05 2008
MATHEMATICA
a=1; lst={a}; k=12; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 17 2008 *)
CROSSREFS
Sequence in context: A155267 A157837 A039367 * A124706 A145990 A089528
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Apr 29 2008
EXTENSIONS
More terms from Emeric Deutsch, May 05 2008
More terms from Colin Barker, Oct 10 2013
STATUS
approved