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 A082685 (2*5^n + 2^n)/3. 6

%I

%S 1,4,18,86,422,2094,10438,52126,260502,1302254,6510758,32552766,

%T 162761782,813804814,4069015878,20345063006,101725282262,508626345774,

%U 2543131597798,12715657726846,63578288109942,317891439501134

%N (2*5^n + 2^n)/3.

%C Binomial transform of A007583

%C Row sums of A114195. - _Paul Barry_, Nov 16 2005

%H Vincenzo Librandi, <a href="/A082685/b082685.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-10)

%F G.f.: (1-3x)/((1-5x)(1-2x))

%F a(n)=sum{k=0..n, sum{j=0..n, C(n, j)C(j+k, 2k)2^(j-k)}}. - _Paul Barry_, Nov 16 2005

%F a(0)=1, a(1)=4, a(n)=7*a(n-1)-10*a(n-2). - _Harvey P. Dale_, Apr 09 2014

%t Table[(2*5^n+2^n)/3,{n,0,30}] (* or *) LinearRecurrence[{7,-10},{1,4},30] (* _Harvey P. Dale_, Apr 09 2014 *)

%t CoefficientList[Series[(1 - 3 x)/((1 - 5 x) (1 - 2 x)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Apr 10 2014 *)

%o (PARI) a(n)=(2*5^n+2^n)/3 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A001045.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Apr 11 2003

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Last modified March 22 04:32 EDT 2019. Contains 321406 sequences. (Running on oeis4.)