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

Author

Benoit Cloitre, Jun 17 2003

Keywords

• nonn

Links

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

Crossrefs

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

Cf. A094200, A094201.

Programs

PARI

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

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)