A346434 Triangle read by rows of numbers with n 1's and n 0's in their representation in base of Fibonacci numbers (A210619), written as those 1's and 0's.

10, 1001, 1010, 100101, 101001, 101010, 10010101, 10100101, 10101001, 10101010, 1001010101, 1010010101, 1010100101, 1010101001, 1010101010, 100101010101, 101001010101, 101010010101, 101010100101, 101010101001, 101010101010

Offset: 1

Author

Kevin Ryde, Jul 18 2021

Keywords

• nonn
• easy
• tabl

Comments

The digits of T(n,k) are k pairs 10 followed by n-k pairs 01.

Examples

			Triangle begins:
        k=1       k=2       k=3       k=4
  n=1:  10
  n=2:  1001,     1010,
  n=3:  100101,   101001,   101010,
  n=4:  10010101, 10100101, 10101001, 10101010
  ...
For n=5,k=3, the 10 and 01 digit pairs are
           vvvvvv          k  = 3 pairs 10
  T(5,3) = 1010100101
                 ^^^^     n-k = 2 pairs 01
		

Links

• Kevin Ryde, Table of n, a(n) for triangle rows 1 to 49, flattened

Crossrefs

Cf. A210619, A163662 (main diagonal), A014417 (Zeckendorf digits).

Programs

PARI

T(n,k) = (10*100^n - 9*100^(n-k)) \ 99;

Formula

T(n,k) = (10*100^n - 9*100^(n-k) - 1)/99, for n>=1 and 1 <= k <= n.

T(n,k) = A014417(A210619(n,k)).

T(n,n) = A163662(n).

G.f.: x*y*(10 - 9*x - 100*x^2*y) / ((1-x) * (1-100*x) * (1-x*y) * (1-100*x*y) ).