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 A099786 Sum C(n-k,3k)3^(n-4k), k=0..floor(n/4). 2
 1, 3, 9, 27, 82, 255, 819, 2727, 9397, 33312, 120537, 441855, 1631017, 6036879, 22345074, 82589247, 304612975, 1120960983, 4116353265, 15088372416, 55224373105, 201895801851, 737506551321, 2692518758163, 9826402960882 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In general a(n)=sum{k=0..floor(n/4), C(n-k,3k)u^k*v^(n-4k)} has g.f. (1-v*x)^2/((1-v*x)^3-u*x^4) and satisfies the recurrence a(n)==3v*a(n-1)-3v^2*a(n-2)+v^3*a(n-3)+u*a(n-4). LINKS Index entries for linear recurrences with constant coefficients, signature (9,-27,27,1). FORMULA G.f.: (1-3x)^2/((1-3x)^3-x^4); a(n)=9a(n-1)-27a(n-2)+27a(n-3)+a(n-4). MATHEMATICA LinearRecurrence[{9, -27, 27, 1}, {1, 3, 9, 27}, 40] (* or *) CoefficientList[ Series[-((1-3 x)^2/(x (x (x (x+27)-27)+9)-1)), {x, 0, 40}], x] (* Harvey P. Dale, Jun 06 2011 *) CROSSREFS Cf. A003522, A097119, A099785, A099787. Sequence in context: A078226 A083591 A052917 * A237272 A192909 A171155 Adjacent sequences:  A099783 A099784 A099785 * A099787 A099788 A099789 KEYWORD easy,nonn AUTHOR Paul Barry, Oct 26 2004 STATUS approved

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