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 A099582 Sum C(n-k,k-1)4^(n-k-1), k=0..floor(n/2). 2
 0, 0, 1, 4, 24, 112, 560, 2688, 13056, 62976, 304384, 1469440, 7096320, 34263040, 165441536, 798818304, 3857055744, 18623496192, 89922273280, 434183077888, 2096421666816, 10122418978816, 48875363631104, 235991130439680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS In general a(n)=sum{k=0..floor(n/2), C(n-k,k-1)r^(n-k-1) has g.f. x^2/((1-r*x^2)(1-r*x-r*x^2)) and satisfies a(n)=r*a(n-1)+2r*a(n-2)-r^2*a(n-3)-r^2*a(n-4). LINKS Index entries for linear recurrences with constant coefficients, signature (4,8,-16,-16). FORMULA G.f.: x^2/((1-4x^2)(1-4x-4x^2)); a(n)=4a(n-1)+8a(n-2)-16a(n-3)-16a(n-4). a(0)=0, a(1)=0, a(2)=1, a(3)=4, a(n)=4*a(n-1)+8*a(n-2)-16*a(n-3)- 16*a(n-4) From Harvey P. Dale, Jul 19 2012 MATHEMATICA Table[Sum[Binomial[n-k, k-1]*4^(n-k-1), {k, 0, Floor[n/2]}], {n, 0, 30}] (* or *) LinearRecurrence[{4, 8, -16, -16}, {0, 0, 1, 4}, 30] (* Harvey P. Dale, Jul 19 2012 *) CROSSREFS Cf. A099177, A099581. Sequence in context: A270686 A272253 A300581 * A295093 A211142 A272735 Adjacent sequences:  A099579 A099580 A099581 * A099583 A099584 A099585 KEYWORD easy,nonn AUTHOR Paul Barry, Oct 23 2004 STATUS approved

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)