Search: id:A055588
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%I A055588
%S A055588 1,2,4,9,22,56,145,378,988,2585,6766,17712,46369,121394,317812,832041,
%T A055588 2178310,5702888,14930353,39088170,102334156,267914297,701408734,
%U A055588 1836311904,4807526977,12586269026,32951280100,86267571273
%N A055588 a(n)=3a(n-1)-a(n-2)-1; a(0)=1, a(1)=2.
%C A055588 Number of directed column-convex polyominoes with area n+2 and having 
               two cells in the bottom row - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Jun 14 2001
%C A055588 a(n) = length of the list generated by the substitution: 3->3, 4->(3,
               4,6), 6->(3,4,6,6): {3, 4}, {3, 3, 4, 6}, {3, 3, 3, 4, 6, 3, 4, 6, 
               6}, {3, 3, 3, 3, 4, 6, 3, 4, 6, 6, 3, 3, 4, 6, 3, 4, 6, 6, 3, 4, 
               6, 6}, etc. - Wouter Meeussen, Nov 23, 2003
%C A055588 Equals row sums of triangle A144955 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Sep 27 2008]
%D A055588 E. Barcucci, R. Pinzani, R. Sprugnoli, Directed column-convex polyominoes 
               by recurrence relations, Lecture Notes in Computer Science, No. 668, 
               Springer, Berlin (1993), pp. 282-298.
%F A055588 a(n)={[((3+sqrt(5))/2)^n-((3-sqrt(5))/2)^n]/sqrt(5)}+1.
%F A055588 a(n)= sum(A055587(n, m), m=0..n) = 1+A001906(n); G.f.: (1-2*x)/((1-3*x+x^2)*(1-x)).
%F A055588 a(n)=4a(n-1)-4a(n-2)+a(n-3); a(n)=sum{k=0..floor(n/3), binomial(n-k, 
               2k)2^(n-3k)}. - Paul Barry (pbarry(AT)wit.ie), Oct 07 2004
%F A055588 a(n)=Fib(2n)+1; a(n)=sum{k=0..n, Fib(2k+2)(2*0^(n-k)-1)}; a(n)=A008346(2n). 
               - Paul Barry (pbarry(AT)wit.ie), Oct 26 2004
%p A055588 g:=z/(1-3*z+z^2): gser:=series(g, z=0, 43): seq(abs(coeff(gser, z, n)+1), 
               n=0..27);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 
               22 2009]
%o A055588 sage: [lucas_number1(n,3,1)+1 for n in range(29)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 06 2008
%Y A055588 Cf. A055587, A001906. Partial sums of A001519.
%Y A055588 Apart from first term, same as A052925.
%Y A055588 A144955 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 27 2008]
%Y A055588 Sequence in context: A098719 A115324 A107092 this_sequence A088456 A152225 
               A091561
%Y A055588 Adjacent sequences: A055585 A055586 A055587 this_sequence A055589 A055590 
               A055591
%K A055588 nonn,easy
%O A055588 0,2
%A A055588 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) May 30 2000, 
               Barry E. Williams, Jun 04 2000

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