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A119336 Expansion of (1-x)^4/((1-x)^6 - x^6). 4

%I

%S 1,2,3,4,5,6,8,16,45,130,341,804,1730,3460,6555,12016,21845,40410,

%T 77540,155080,320001,669526,1398101,2884776,5858126,11716252,23166783,

%U 45536404,89478485,176565486,350739488,701478976,1410132405,2841788170

%N Expansion of (1-x)^4/((1-x)^6 - x^6).

%C Row sums of A119335. Binomial transform of (1+x)/(1-x)^6.

%C Equals binomial transform of [1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1,...]. - _Gary W. Adamson_, Mar 14 2009

%H Harvey P. Dale, <a href="/A119336/b119336.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6).

%F a(n) = Sum_{k=0..n} Sum_{j=0..n-k} C(k,3j)*C(n-k,3j).

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5), with a(0)=1, a(1)=2, a(2)=3, a(3)=4, a(4)=5. - _Harvey P. Dale_, Dec 25 2015

%F a(n) = Sum_{k=0..floor(n/6)} binomial(n+1,6*k+1). - _Seiichi Manyama_, Mar 22 2019

%t CoefficientList[Series[(1-x)^4/((1-x)^6-x^6),{x,0,40}],x] (* or *) LinearRecurrence[{6,-15,20,-15,6},{1,2,3,4,5},40] (* _Harvey P. Dale_, Dec 25 2015 *)

%o (PARI) {a(n) = sum(k=0, n\6, binomial(n+1, 6*k+1))} \\ _Seiichi Manyama_, Mar 22 2019

%Y Cf. A119335, A306847.

%K easy,nonn

%O 0,2

%A _Paul Barry_, May 14 2006

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Last modified May 18 00:43 EDT 2021. Contains 343992 sequences. (Running on oeis4.)