This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.