OFFSET
1,3
COMMENTS
T(n,m) is the triangle read by rows, 0<=m<n.
A118965 and A066853 give numbers of zeros and nonzeros in n-th row, respectively. - Reinhard Zumkeller, Jan 16 2014
LINKS
Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened
G. Darvasi and St. Eckmann, Zur Verteilung der Reste der Fibonacci-Folge modulo 5c, Elemente der Mathematik 50 (1995) pp. 76-80.
FORMULA
T(n,n) = A235715(n). - Reinhard Zumkeller, Jan 17 2014
EXAMPLE
{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,
MAPLE
MATHEMATICA
A001175[1] = 1; A001175[n_] := For[k = 1, True, k++, If[Mod[Fibonacci[k], n] == 0 && Mod[Fibonacci[k+1], n] == 1, Return[k]]]; T[m_, h_] := Module[{resul, k, M}, resul = 0; For[k = 0, k <= A001175[m]-1, k++, M = Mod[Fibonacci[k], m]; If[ M == h, resul++]]; Return[resul]]; Table[T[m, h], {m, 1, 17}, {h, 0, m-1}] // Flatten (* Jean-François Alcover, Feb 11 2015, after Maple code *)
PROG
(Haskell)
import Data.List (group, sort)
a128924 n k = a128924_tabl !! (n-1) !! (k-1)
a128924_tabl = map a128924_row [1..]
a128924_row 1 = [1]
a128924_row n = f [0..n-1] $ group $ sort $ g 1 ps where
f [] _ = []
f (v:vs) wss'@(ws:wss) | head ws == v = length ws : f vs wss
| otherwise = 0 : f vs wss'
g 0 (1 : xs) = []
g _ (x : xs) = x : g x xs
ps = 1 : 1 : zipWith (\u v -> (u + v) `mod` n) (tail ps) ps
-- Reinhard Zumkeller, Jan 16 2014
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. J. Mathar, Apr 25 2007
STATUS
approved