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A115291 Expansion of (1+x)^3/(1-x). 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 (list; graph; refs; listen; history; text; internal format)
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,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

Also continued fraction expansion of (132-sqrt(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) = 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).

MATHEMATICA

CoefficientList[Series[(1+x)^3/(1-x), {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

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Last modified December 12 01:08 EST 2017. Contains 295936 sequences.