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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 (list; graph; refs; listen; history; text; internal format)
 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 LINKS Table of n, a(n) for n=1..31. Index entries for linear recurrences with constant coefficients, signature (3,-2). 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 Cf. A139634, A139635. Sequence in context: A155267 A157837 A039367 * A124706 A145990 A089528 Adjacent sequences: A139694 A139695 A139696 * A139698 A139699 A139700 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

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Last modified August 14 05:41 EDT 2024. Contains 375146 sequences. (Running on oeis4.)