

A115291


Expansion of (1+x)^3/(1x).


14



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, 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, 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
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OFFSET

0,2


COMMENTS

Partial sums are A086570. Partial sums of squares are A115295. Correlation triangle is A115292.
Let m=4. We observe that a(n)=sum{C(m,n2*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)^(m1)/(1z).  Richard Choulet, Dec 08 2009
Also continued fraction expansion of (132sqrt(17))/103. _ Bruno Berselli_, Sep 23 2011
Also decimal expansion of 1331/9000.  Vincenzo Librandi, Sep 23 2011


LINKS

Table of n, a(n) for n=0..104.
Index entries for linear recurrences with constant coefficients, signature (1).


FORMULA

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


MATHEMATICA

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


CROSSREFS

Cf. A040000, A113311, A171418, A171440, A171441, A171442, A171443.
Sequence in context: A272490 A261654 A121488 * A108615 A090383 A179620
Adjacent sequences: A115288 A115289 A115290 * A115292 A115293 A115294


KEYWORD

nonn,easy


AUTHOR

Paul Barry, Jan 19 2006


STATUS

approved



