0,2

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

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

Equals row sums of triangle A144955 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 27 2008]

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.

a(n)={[((3+sqrt(5))/2)^n-((3-sqrt(5))/2)^n]/sqrt(5)}+1.

a(n)= sum(A055587(n, m), m=0..n) = 1+A001906(n); G.f.: (1-2*x)/((1-3*x+x^2)*(1-x)).

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

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

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]

sage: [lucas_number1(n, 3, 1)+1 for n in range(29)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 06 2008

Cf. A055587, A001906. Partial sums of A001519.

Apart from first term, same as A052925.

A144955 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 27 2008]

Sequence in context: A098719 A115324 A107092 this_sequence A088456 A152225 A091561

Adjacent sequences: A055585 A055586 A055587 this_sequence A055589 A055590 A055591

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) May 30 2000, Barry E. Williams, Jun 04 2000