Search: id:A097076
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%I A097076
%S A097076 0,1,1,4,8,21,49,120,288,697,1681,4060,9800,23661,57121,137904,332928,
%T A097076 803761,1940449,4684660,11309768,27304197,65918161,159140520,384199200,
%U A097076 927538921,2239277041,5406093004,13051463048,31509019101,76069501249
%N A097076 Expansion of x/(1-x-3x^2-x^3).
%C A097076 Counts walks of length n between two vertices of a triangle, when a loop 
               has been added at the third vertex.
%C A097076 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
%C A097076 Starting (1, 1, 4, 8, 21,...) = row sums of triangle A157898 [From Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), Mar 08 2009]
%C A097076 Convolution of Pell(n)=A000129(n) and (-1)^n. [From Paul Barry (pbarry(AT)wit.ie), 
               Oct 22 2009]
%F A097076 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.
%F A097076 a(n)=sum{k=0..n, (-1)^k*Pell(n-k)}. [From Paul Barry (pbarry(AT)wit.ie), 
               Oct 22 2009]
%Y A097076 Cf. A000129, A051927, A097075.
%Y A097076 A157898 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 08 2009]
%Y A097076 Sequence in context: A079860 A006908 A061256 this_sequence A077921 A003608 
               A129794
%Y A097076 Adjacent sequences: A097073 A097074 A097075 this_sequence A097077 A097078 
               A097079
%K A097076 easy,nonn
%O A097076 0,4
%A A097076 Paul Barry (pbarry(AT)wit.ie), Jul 22 2004

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