A114195 -id:A114195 - cp's OEIS frontend

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

1, 4, 18, 86, 422, 2094, 10438, 52126, 260502, 1302254, 6510758, 32552766, 162761782, 813804814, 4069015878, 20345063006, 101725282262, 508626345774, 2543131597798, 12715657726846, 63578288109942, 317891439501134

Offset: 0

Paul Barry, Apr 11 2003

Binomial transform of A007583

Row sums of A114195. - Paul Barry, Nov 16 2005

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-10)

Cf. A001045.

Table[(2*5^n+2^n)/3,{n,0,30}] (* or *) LinearRecurrence[{7,-10},{1,4},30] (* Harvey P. Dale, Apr 09 2014 *)
CoefficientList[Series[(1 - 3 x)/((1 - 5 x) (1 - 2 x)), {x, 0, 50}], x] (* Vincenzo Librandi, Apr 10 2014 *)

a(n)=(2*5^n+2^n)/3 \\ Charles R Greathouse IV, Oct 07 2015

G.f.: (1-3x)/((1-5x)(1-2x))
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
a(0)=1, a(1)=4, a(n)=7*a(n-1)-10*a(n-2). - Harvey P. Dale, Apr 09 2014

A114196 Expansion of (1-3x)/(1-6x+8x^2+x^3).

Original entry on oeis.org

1, 3, 10, 35, 127, 472, 1781, 6783, 25978, 99823, 384331, 1481424, 5714073, 22048715, 85098282, 328485899, 1268080423, 4895497064, 18899853101, 72967061671, 281708048154, 1087611942455, 4199040207827, 16211637659168

Offset: 0

Paul Barry, Nov 16 2005

Diagonal sums of A114195.

Index entries for linear recurrences with constant coefficients, signature (6, -8, -1).

CoefficientList[Series[(1-3x)/(1-6x+8x^2+x^3),{x,0,30}],x] (* or *) LinearRecurrence[{6,-8,-1},{1,3,10},30] (* Harvey P. Dale, Feb 02 2012 *)

a(n)=6a(n-1)-8a(n-2)-a(n-3); a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(n-k, j)C(j+k, 2k)2^(j-k)}}.

cp's OEIS Frontend

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

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