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A133124
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A007318 * [1, 2, 2, 3, 2, 3, 2, 3, 2, ...].
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5
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1, 3, 7, 16, 35, 74, 153, 312, 631, 1270, 2549, 5108, 10227, 20466, 40945, 81904, 163823, 327662, 655341, 1310700, 2621419, 5242858, 10485737, 20971496, 41943015, 83886054, 167772133, 335544292, 671088611, 1342177250, 2684354529, 5368709088, 10737418207, 21474836446
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OFFSET
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0,2
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LINKS
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FORMULA
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Binomial transform of [1, 2, 2, 3, 2, 3, 2, 3, 2, ...].
a(n) = 5*2^(n-1) - (n+1), for n >= 1.
G.f.: 1 + x*(3-5*x+3*x^2)/((1-2*x)*(1-x)^2). - R. J. Mathar, Nov 14 2007
E.g.f.: (5*exp(2*x) - 2*(1+x)*exp(x) - 1)/2. - G. C. Greubel, Oct 21 2017
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EXAMPLE
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a(3) = (1, 3, 3, 1) dot (1, 2, 2, 3) = (1 + 6 + 6 + 3).
a(5) = 74 = 2^6 + 2^4 - 6 = 64 + 16 - 6.
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MATHEMATICA
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Join[{1}, Table[5*2^(n-1) - n -1, {n, 1, 50)]] (* G. C. Greubel, Oct 21 2017 *)
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PROG
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(PARI) concat(1, for(n=1, 50, print1(5*2^(n - 1) - n - 1, ", "))) \\ G. C. Greubel, Oct 21 2017
(Magma) [1] cat [5*2^(n - 1) - n -1: n in [1..50]]; // G. C. Greubel, Oct 21 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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