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A097076 Expansion of x/(1-x-3x^2-x^3). +0
7
0, 1, 1, 4, 8, 21, 49, 120, 288, 697, 1681, 4060, 9800, 23661, 57121, 137904, 332928, 803761, 1940449, 4684660, 11309768, 27304197, 65918161, 159140520, 384199200, 927538921, 2239277041, 5406093004, 13051463048, 31509019101, 76069501249 (list; graph; listen)
OFFSET

0,4

COMMENT

Counts walks of length n between two vertices of a triangle, when a loop has been added at the third vertex.

a(n) = center term of the 3x3 matrix [0,1,0; 0,0,1; 1,3,1]^n - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 30 2008

FORMULA

a(n)=a(n)=(1+sqrt(2))^n/4+(1-sqrt(2))^n/4-(-1)^n/2; a(n)=a(n-1)+3a(n-2)+a(n-3) [corrected by Paul Curtz, Mar 04 2008]; a(n)=sum{k=0..floor(n/2), binomial(n, 2k)2^k}/2-(-1)^n/2. a(n)=A001333(n)/2-(-1)^n/2.

CROSSREFS

Cf. A000129, A051927, A097075.

Sequence in context: A079860 A006908 A061256 this_sequence A077921 A003608 A129794

Adjacent sequences: A097073 A097074 A097075 this_sequence A097077 A097078 A097079

KEYWORD

easy,nonn

AUTHOR

Paul Barry (pbarry(AT)wit.ie), Jul 22 2004

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.


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