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A077834
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Expansion of 1/(1-2*x-2*x^2-3*x^3).
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3
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1, 2, 6, 19, 56, 168, 505, 1514, 4542, 13627, 40880, 122640, 367921, 1103762, 3311286, 9933859, 29801576, 89404728, 268214185, 804642554, 2413927662, 7241782987, 21725348960, 65176046880, 195528140641, 586584421922, 1759753265766, 5279259797299, 15837779391896
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (2,2,3)
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FORMULA
| Convolution of A000244 and A049347. G.f. : 1/((1-3x)(1+x+x^2)); a(n)=sum{k=0..n, 3^k*2sqrt(3)cos(2*pi*(n-k)/3+pi/6)/3}; a(n)=3^(n+2)/13+2sqrt(3)cos(2*pi*n/3+pi/6)/39+2sqrt(3)sin(2*pi*n/3+pi/3)/13. - Paul Barry (pbarry(AT)wit.ie), May 19 2004
a(n) = A152733(n+3)/3. [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
a(0)=1, a(1)=2, a(2)=6, a(n)=2*a(n-1)+2*a(n-2)+3*a(n-3) [From Harvey P. Dale, Jan 31 2012]
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MAPLE
| A049347 := proc(n) op(1+(n mod 3), [1, -1, 0]) ; end proc:
A077834 := proc(n) (3^(n+2)+3*A049347(n-1)+4*A049347(n))/13 ; end proc:
seq(A077834(n), n=0..20) ; # R. J. Mathar, Mar 22 2011
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MATHEMATICA
| k0=k1=0; lst={}; Do[kt=k1; k1=3^n-k1-k0; k0=kt; AppendTo[lst, k1/3], {n, 1, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
CoefficientList[Series[1/(1-2x-2x^2-3x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[{2, 2, 3}, {1, 2, 6}, 30] (* From Harvey P. Dale, Jan 31 2012 *)
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CROSSREFS
| Sequence in context: A183305 A192715 A121483 * A067675 A037512 A111277
Adjacent sequences: A077831 A077832 A077833 * A077835 A077836 A077837
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002
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