A231335 Number of distinct Fibonacci numbers in rows of triangle A230871.

1, 1, 2, 2, 3, 3, 3, 4, 3, 3, 5, 4, 3, 4, 6, 4, 5, 4, 5, 6, 5, 4, 6, 7, 4, 5

Offset: 0

Author

Reinhard Zumkeller, Nov 07 2013

Keywords

• nonn
• more

Comments

a(n) = Sum_{k=1..A231331(n)} A010056(A231330(n,k));

a(n) > 1 for n > 1.

Examples

			a(0) = #{0} = 1;
a(1) = #{1} = 1;
a(2) = #{1, 3} = 2;
a(3) = #{2, 8} = 2;
a(4) = #{3, 5, 21} = 3;
a(5) = #{5, 13, 55} = 3;
a(6) = #{8, 34, 144} = 3;
a(7) = #{13, 55, 89, 377} = 4;
a(8) = #{21, 233, 987} = 3;
a(9) = #{34, 610, 2584} = 3;
a(10) = #{55, 89, 377, 1597, 6765} = 5;
a(11) = #{89, 377, 4181, 17711} = 4;
a(12) = #{144, 10946, 46368} = 3;
a(13) = #{233, 1597, 28657, 121393} = 4;
a(14) = #{377, 987, 1597, 6765, 75025, 317811} = 6;
a(15) = #{610, 10946, 196418, 832040} = 4;
a(16) = #{987, 4181, 6765, 514229, 2178309} = 5.
		

Crossrefs

Cf. A000045, A010056, A230871, A231330, A231331.

Programs

Haskell

a231335 = length . filter ((== 1) . a010056) . a231330_row

PARI

isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || issquare(k-8);
vf(v) = #select(isfib, Set(v));
lista(nn) = my(va=[0], vb=[1]); print1(vf(va), ", "); print1(vf(vb), ", "); for (n=2, nn, v = vector(2^(n-1), k, j=(k+1)\2; i=(j+1)\2; y=vb[j]; x=va[i]; if (k%2, y+x, 3*y-x)); print1(vf(v), ", "); va = vb; vb = v;); \\ Michel Marcus, Sep 23 2023

Extensions

a(19)-a(25) from Michel Marcus, Sep 23 2023