|
|
A061667
|
|
a(n) = Fibonacci(2*n+1) - 2^(n-1).
|
|
14
|
|
|
1, 3, 9, 26, 73, 201, 546, 1469, 3925, 10434, 27633, 72977, 192322, 506037, 1329885, 3491810, 9161929, 24026745, 62983842, 165055853, 432445861, 1132806018, 2967020769, 7770353441, 20348233858, 53282736741, 139516753581, 365301078434, 956453590585
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Number of cells in the bottom row of all directed column-convex polyominoes of area n+1.
Also the binomial transform of A000071 (after removing its 2 leading zeros). - R. J. Mathar, Nov 04 2008
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x*(1-x)^2/((1-2*x)*(1-3*x+x^2)). - corrected by Philip B. Zhang, Nov 28 2014
a(n) = Sum_{k=0..n+1} C(n+1, k)*sum{j=0..floor(k/2), Fibonacci(k-2j)}. - Paul Barry, Apr 17 2005
a(n) = 2^(-1-n)*(-5*4^n - (3-sqrt(5))^n*(-5+sqrt(5)) + (3+sqrt(5))^n*(5+sqrt(5))) / 5.
a(n) = 5*a(n-1) - 7*a(n-2) + 2*a(n-3) for n>3. (End)
|
|
MATHEMATICA
|
|
|
PROG
|
(PARI) { for (n=1, 200, write("b061667.txt", n, " ", fibonacci(2*n + 1) - 2^(n - 1))) } \\ Harry J. Smith, Jul 26 2009
(PARI) Vec(x*(1-x)^2/((1-2*x)*(1-3*x+x^2)) + O(x^50)) \\ Michel Marcus, Nov 29 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|