A147561 Number of representations of n in the Fibonacci-squared base system. The columns are ..., 64, 25, 9, 4, 1, 1 = ..., 8^2, 5^2, 3^2, 2^2, 1^2, 1^2, i.e., the Fibonacci numbers A000045 squared. The 'digits' are 0, 1 or 2.

2, 3, 2, 2, 2, 3, 2, 2, 3, 5, 5, 3, 2, 2, 3, 2, 2, 3, 5, 5, 3, 2, 2, 3, 3, 4, 5, 5, 4, 3, 3, 2, 2, 3, 5, 5, 3, 2, 2, 3, 2, 2, 3, 5, 5, 3, 2, 2, 3, 3, 4, 5, 5, 4, 3, 3, 2, 2, 3, 5, 5, 3, 2, 3, 5, 5, 4, 5, 7, 8, 5, 4, 5, 8, 7, 5, 4, 5, 5, 3, 2, 3, 5, 5, 3, 2, 2, 3, 3, 4, 5, 5, 4, 3, 3, 2, 2, 3, 5, 5

Offset

1,1

Comments

Note there are two columns labeled 1.

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Ron Knott, Fibonacci Bases: The Fibonacci^2 Base System

Example

a(2) = 3 since 2 is 02, 20 and 11 using both columns labeled 1;
a(10) = 5 because 10 = 9 + 1 with 2 Fib-sq reps 1010, 1001; 10 = 2*4 + 2 with 3 Fib-sq reps 220, 211 and 202; so there are in total 5 Fib-sq representations for 10.

Prog

(PARI) first(n) = {my(fib2list = List(), fib2 = 1, t = 1, res = vector(n)); while(fib2 <= n, listput(fib2list, fib2); t++; fib2 = fibonacci(t)^2); for(i=1, 3^#fib2list-1, b = digits(i, 3); b = concat(vector(#fib2list-#b), b); s = sum(i=1, #b, b[i]*fib2list[i]); if(s<=n, res[s]++)); res} \\ David A. Corneth, Jul 24 2017

Crossrefs

Cf. A000045, A007598.

Sequence in context: A185049 A186181 A324983 * A210659 A103266 A185150

Adjacent sequences: A147558 A147559 A147560 * A147562 A147563 A147564

Keyword

nonn,base,look

Author

Ron Knott, Nov 07 2008

Status

approved