A085005 A Von Koch curve related to the Golden ratio.

1, 3, 4, 4, 3, 3, 4, 4, 3, 1, 0, 0, 1, 1, 0, 0, 1, 3, 4, 4, 5, 7, 10, 12, 13, 13, 14, 16, 17, 17, 16, 16, 17, 19, 20, 20, 21, 23, 26, 28, 29, 31, 34, 38, 41, 43, 44, 46, 49, 51, 52, 52, 53, 55, 56, 56, 55, 55, 56, 58, 59, 59, 60, 62, 65, 67, 68, 68, 69, 71, 72, 72, 71, 71, 72, 72, 71

Offset

1,2

Links

Table of n, a(n) for n=1..77.

Benoit Cloitre, Plot of a(n) for n=1 up to 1362772

Formula

a(n)=(-1)*sum(i=1, n, sum(j=1, i, (-1)^floor(j*(1+sqrt(5))/2)))

a(n) = 2*sum(k = 1, n, sum(i = 1, k, b(i)))-n*(n+1)/2, where b(k) = floor(phi*k)-2*floor(phi*k/2)

Prog

(PARI) a(n)=(-1)*sum(i=1, n, sum(j=1, i, (-1)^floor(j*(1+sqrt(5))/2)))

Crossrefs

Cf. A083035, A083036, A083037, A083038, A085002, A085003, A085004.

Cf. A094200, A094201.

Sequence in context: A334492 A306571 A019917 * A370454 A306477 A276865

Adjacent sequences: A085002 A085003 A085004 * A085006 A085007 A085008

Keyword

nonn

Author

Benoit Cloitre, Jun 17 2003

Status

approved