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

0,3

Comments

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

a(n) > 1 for n > 1.

Links

Table of n, a(n) for n=0..25.

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A270920 A262956 A073734 * A271237 A062558 A072789

Adjacent sequences: A231332 A231333 A231334 * A231336 A231337 A231338

Keyword

nonn,more

Author

Reinhard Zumkeller, Nov 07 2013

Extensions

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

Status

approved