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A054963
Number of cells in the first column of all directed column-convex polyominoes of area n+1.
1
1, 3, 9, 26, 72, 194, 515, 1357, 3563, 9340, 24466, 64068, 167749, 439191, 1149837, 3010334, 7881180, 20633222, 54018503, 141422305, 370248431, 969323008, 2537720614, 6643838856, 17393795977, 45537549099, 119218851345
OFFSET
0,2
LINKS
E. Barcucci, R. Pinzani and R. Sprugnoli, Directed column-convex polyominoes by recurrence relations, Lecture Notes in Computer Science, No. 668, Springer, Berlin (1993), pp. 282-298.
FORMULA
a(n) = Fibonacci(2*n) + Fibonacci(2*n+2) - n = A002878(n)-n.
G.f.: (1-2x+2x^2)/((1-x)^2(1-3x+x^2)).
a(n) = 5*a(n-1) - 8*a(n-2) + 5*a(n-3) - a(n-4) for n >= 4. - Jinyuan Wang, Mar 10 2020
PROG
(PARI) Vec((1-2*x+2*x^2)/((1-x)^2*(1-3*x+x^2)) + O(x^40)) \\ Michel Marcus, Feb 14 2016
CROSSREFS
Cf. A000045.
Sequence in context: A138237 A121286 A072863 * A291733 A118046 A057153
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jun 16 2001
STATUS
approved