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A159694
a(n) = 2*a(n-1) + 2^(n-1), for n > 0, with a(0)=6.
8
6, 13, 28, 60, 128, 272, 576, 1216, 2560, 5376, 11264, 23552, 49152, 102400, 212992, 442368, 917504, 1900544, 3932160, 8126464, 16777216, 34603008, 71303168, 146800640, 301989888, 620756992, 1275068416, 2617245696, 5368709120
OFFSET
0,1
COMMENTS
Diagonal of triangles A062111, A152920.
LINKS
Milan Janjić and Boris Petković, A Counting Function, arXiv:1301.4550 [math.CO], 2013.
Milan Janjić and Boris Petković, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq., Vol. 17 (2014), Article 14.3.5.
FORMULA
a(n) = Sum_{k=0..n} (k+6)*binomial(n,k).
From Klaus Brockhaus, Sep 27 2009: (Start)
a(n) = (6 + n/2)*2^n.
G.f.: (6 - 11*x)/(1-2*x)^2. (End)
From Amiram Eldar, Jan 19 2021: (Start)
Sum_{n>=0} 1/a(n) = 8192*log(2) - 3934820/693.
Sum_{n>=0} (-1)^n/a(n) = 11509636/3465 - 8192*log(3/2). (End)
E.g.f.: (6 + x)*exp(2*x). - G. C. Greubel, Sep 27 2022
EXAMPLE
a(0) = 6,
a(1) = 2* 6 + 1 = 13,
a(2) = 2*13 + 2 = 28,
a(3) = 2*28 + 4 = 60,
a(4) = 2*60 + 8 = 128, ...
MATHEMATICA
Table[(6 + n/2)*2^n, {n, 0, 30}] (* Amiram Eldar, Jan 19 2021 *)
PROG
(Magma) [(12+n)*2^(n-1): n in [0..30]]; // G. C. Greubel, Sep 27 2022
(SageMath) [(12+n)*2^(n-1) for n in range(30)] # G. C. Greubel, Sep 27 2022
CROSSREFS
Seventh row of triangle A062111. - Klaus Brockhaus, Sep 27 2009
Sequence in context: A116913 A016071 A086652 * A145976 A101622 A256871
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Apr 20 2009
STATUS
approved