OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
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.
Index entries for linear recurrences with constant coefficients, signature (4,-4).
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
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Apr 20 2009
STATUS
approved