|
|
A085601
|
|
a(n) = 2 * (4^n + 2^n) + 1.
|
|
26
|
|
|
5, 13, 41, 145, 545, 2113, 8321, 33025, 131585, 525313, 2099201, 8392705, 33562625, 134234113, 536903681, 2147549185, 8590065665, 34360000513, 137439477761, 549756862465, 2199025352705, 8796097216513, 35184380477441
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
1. Begin with a square tile.
2. Place square tiles on each edge to form a diamond shape.
3. Count the tiles: a(0) = 5.
4. Add tiles to fill the enclosing square.
5. Go to step 2.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3).
G.f.: -(5 - 22*x + 20*x^2)/((x - 1)*(2*x - 1)*(4*x - 1)).
(End)
E.g.f.: e^x + 2*(e^(2*x) + e^(4*x)). - Iain Fox, Dec 30 2017
|
|
MATHEMATICA
|
Table[2(4^n+2^n)+1, {n, 0, 30}] (* or *) LinearRecurrence[{7, -14, 8}, {5, 13, 41}, 30] (* Harvey P. Dale, Dec 30 2017 *)
|
|
PROG
|
(PARI) first(n) = Vec((5 - 22*x + 20*x^2)/(1 - 7*x + 14*x^2 - 8*x^3) + O(x^n)) \\ Iain Fox, Dec 30 2017
|
|
CROSSREFS
|
Cf. A343175 (essentially the same).
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jul 07 2003
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|