A231335 - OEIS

%I #13 Sep 23 2023 07:31:22

%S 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

%N Number of distinct Fibonacci numbers in rows of triangle A230871.

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

%C a(n) > 1 for n > 1.

%e a(0) = #{0} = 1;

%e a(1) = #{1} = 1;

%e a(2) = #{1, 3} = 2;

%e a(3) = #{2, 8} = 2;

%e a(4) = #{3, 5, 21} = 3;

%e a(5) = #{5, 13, 55} = 3;

%e a(6) = #{8, 34, 144} = 3;

%e a(7) = #{13, 55, 89, 377} = 4;

%e a(8) = #{21, 233, 987} = 3;

%e a(9) = #{34, 610, 2584} = 3;

%e a(10) = #{55, 89, 377, 1597, 6765} = 5;

%e a(11) = #{89, 377, 4181, 17711} = 4;

%e a(12) = #{144, 10946, 46368} = 3;

%e a(13) = #{233, 1597, 28657, 121393} = 4;

%e a(14) = #{377, 987, 1597, 6765, 75025, 317811} = 6;

%e a(15) = #{610, 10946, 196418, 832040} = 4;

%e a(16) = #{987, 4181, 6765, 514229, 2178309} = 5.

%o (Haskell)

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

%o (PARI) isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || issquare(k-8);

%o vf(v) = #select(isfib, Set(v));

%o 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

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

%K nonn,more

%O 0,3

%A _Reinhard Zumkeller_, Nov 07 2013

%E a(19)-a(25) from _Michel Marcus_, Sep 23 2023