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

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

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_{k=0..floor(n/2)} C(m,n-2*k). 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: A261654 A332504 A121488 * A108615 A310937 A090383

Adjacent sequences: A115288 A115289 A115290 * A115292 A115293 A115294

Keyword

nonn,easy

Author

Paul Barry, Jan 19 2006

Status

approved