A092263 a(1)=1, a(n+1)=ceiling(phi*a(n))+1 if a(n) is odd, a(n+1)=ceiling(phi*a(n)) if a(n) is even, where phi=(1+sqrt(5))/2.

1, 3, 6, 10, 17, 29, 48, 78, 127, 207, 336, 544, 881, 1427, 2310, 3738, 6049, 9789, 15840, 25630, 41471, 67103, 108576, 175680, 284257, 459939, 744198, 1204138, 1948337, 3152477, 5100816, 8253294, 13354111, 21607407, 34961520, 56568928

Offset

1,2

Comments

Closely related to A079472 for terms with an even row. - Thomas Baruchel, Jul 28 2005

Links

Table of n, a(n) for n=1..36.

Formula

For n>1, a(n) = floor(phi^n*(14+6*sqrt(5))/10) -1

(1/10) {4*Lucas(n+3) - 2(-1)^[n/2] - (-1)^[(n-1)/2] - 15 }. - Ralf Stephan, Dec 02 2004

From Chai Wah Wu, Jan 23 2020: (Start)

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-5) for n > 5.

G.f.: x*(x^2 + x + 1)/((x - 1)*(x^2 + 1)*(x^2 + x - 1)). (End)

Crossrefs

Sequence in context: A005045 A189376 A069241 * A259968 A242525 A266617

Adjacent sequences: A092260 A092261 A092262 * A092264 A092265 A092266

Keyword

nonn

Author

Benoit Cloitre, Feb 18 2004

Status

approved