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A115291 Expansion of (1+x)^3/(1-x). 15

%I

%S 1,4,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,

%T 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,

%U 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8

%N Expansion of (1+x)^3/(1-x).

%C Partial sums are A086570. Partial sums of squares are A115295. Correlation triangle is A115292.

%C Let m=4. We observe that a(n)=sum{C(m,n-2*k),k=0..floor(n/2)). Then there is a link with A113311 and A040000: it is the same formula with respectively m=3 and m=2. We can generalize this result with the sequence whose G.f is given by (1+z)^(m-1)/(1-z). - _Richard Choulet_, Dec 08 2009

%C Also continued fraction expansion of (132-sqrt(17))/103. -_ Bruno Berselli_, Sep 23 2011

%C Also decimal expansion of 1331/9000. - _Vincenzo Librandi_, Sep 23 2011

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%F a(n) = 8-C(2, n)-2*C(1, n)-4*C(0, n); a(n) = sum{k=0..n, C(3, k)}; a(n) = A004070(n, 3).

%t CoefficientList[Series[(1+x)^3/(1-x),{x,0,100}],x] (* or *) PadRight[ {1,4,7},120,{8}] (* _Harvey P. Dale_, May 23 2016 *)

%Y Cf. A040000, A113311, A171418, A171440, A171441, A171442, A171443.

%K nonn,easy

%O 0,2

%A _Paul Barry_, Jan 19 2006

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Last modified October 15 14:07 EDT 2018. Contains 316236 sequences. (Running on oeis4.)