1,3

T(n,m) is the triangle read by rows, 0<=m<n. First column is A001176. Row sums are A001175.

G. Darvasi and St. Eckmann, Zur Verteilung der Reste der Fibonacci-Folge modulo 5c, Elemente der Mathematik 50 (1995) pp. 76-80.

{F(k) mod 4} has fundamental period (0,1,1,2,3,1), see A079343, with

T(4,0)=1 zero, T(4,1)=3 ones, T(4,2)=1 two's, T(4,3)=1 three's. The triangle starts

1,

1, 2,

2, 3, 3,

1, 3, 1, 1,

4, 4, 4, 4, 4,

2, 6, 3, 4, 3, 6,

2, 4, 2, 1, 1, 2, 4,

2, 3, 2, 1, 0, 3, 0, 1,

2, 5, 2, 2, 2, 2, 2, 2, 5,

4, 8, 4, 8, 4, 8, 4, 8, 4, 8,

1, 3, 2, 1, 0, 1, 0, 0, 1, 0, 1,

2, 5, 2, 2, 1, 5, 0, 1, 1, 2, 2, 1,

4, 4, 2, 2, 0, 4, 0, 0, 4, 0, 2, 2, 4,

2, 8, 2, 2, 1, 4, 4, 4, 4, 4, 1, 2, 2, 8,

2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3,

2, 3, 4, 1, 0, 3, 0, 1, 2, 3, 0, 1, 0, 3, 0, 1,

4, 4, 2, 2, 4, 2, 0, 0, 2, 2, 0, 0, 2, 4, 2, 2, 4,

A001175 := proc(n) op(n, [1, 3, 8, 6, 20, 24, 16, 12, 24, 60, 10, 24, 28, 48, 40, 24, 36, 24, 18, 60, 16, 30, 48, 24, 100, 84]) ; end: T := proc(m, h) local resul, k, M ; resul :=0 ; for k from 0 to A001175(m)-1 do M := combinat[fibonacci](k) mod m ; if M = h then resul := resul+1 ; fi ; od ; RETURN(resul) ; end: for m from 1 to 17 do for h from 0 to m-1 do printf("%d, ", T(m, h)) ; od ; printf(" ") ; od;

Sequence in context: A135695 A105899 A071434 this_sequence A116464 A125585 A109973

Adjacent sequences: A128921 A128922 A128923 this_sequence A128925 A128926 A128927

nonn,tabl

R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 25 2007