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 A139698 Binomial transform of [1, 25, 25, 25, ...]. 7
 1, 26, 76, 176, 376, 776, 1576, 3176, 6376, 12776, 25576, 51176, 102376, 204776, 409576, 819176, 1638376, 3276776, 6553576, 13107176, 26214376, 52428776, 104857576, 209715176, 419430376, 838860776, 1677721576, 3355443176, 6710886376, 13421772776, 26843545576 (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 Harvey P. Dale, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (3,-2). FORMULA A007318 * [1, 25, 25, 25, ...]. a(n) = 25*2^(n-1)-24. - Emeric Deutsch, May 03 2008 a(n) = 2*a(n-1) + 24 (with a(1)=1). - Vincenzo Librandi, Nov 24 2010 a(n) = 3*a(n-1)-2*a(n-2). G.f.: x*(23*x+1) / ((x-1)*(2*x-1)). - Colin Barker, Mar 11 2014 EXAMPLE a(3) = 76 = (1, 2, 1) dot (1, 25, 25) = (1 + 50 + 25). MAPLE seq(25*2^(n-1)-24, n=1..25); # Emeric Deutsch, May 03 2008 MATHEMATICA LinearRecurrence[{3, -2}, {1, 26}, 40] (* Harvey P. Dale, Jul 25 2021 *) PROG (PARI) Vec(x*(23*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 11 2014 (Magma) [25*2^(n-1)-24 : n in [1..40]]; // Wesley Ivan Hurt, Jan 17 2017 CROSSREFS Cf. A139634, A139635, A139697. Sequence in context: A251074 A304657 A262221 * A124719 A126380 A083578 Adjacent sequences: A139695 A139696 A139697 * A139699 A139700 A139701 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

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Last modified December 11 02:45 EST 2023. Contains 367717 sequences. (Running on oeis4.)