A333907 - OEIS

%I #24 Mar 16 2021 05:39:59

%S 0,0,1,1,2,3,2,4,7,8,7,4,7,13,17,19,19,17,13,7,12,23,32,39,44,47,48,

%T 47,44,39,32,23,12,20,39,56,71,84,95,104,111,116,119,120,119,116,111,

%U 104,95,84,71,56,39,20,33,65,95,123,149,173,195,215,233,249,263,275

%N For n >= 1, a(n) = Sum_{k=1..n} prevfib(k) + nextfib(k) - 2*k, where prevfib(k) is the largest Fibonacci number < k, nextfib(k) is the smallest Fibonacci number > k.

%e a(1) = (0 + 2 - 2*1) = 0;

%e a(2) = (0 + 2 - 2*1) + (1 + 3 - 2*2) = 0;

%e a(3) = (0 + 2 - 2*1) + (1 + 3 - 2*2) + (2 + 5 - 2*3) = 1;

%e a(4) = (0 + 2 - 2*1) + (1 + 3 - 2*2) + (2 + 5 - 2*3) + (3 + 5 - 2*4) = 1.

%o (PARI) isfib(k) = my(m=5*k^2); issquare(m-4) || issquare(m+4);

%o nextfib(n) = my(k=n+1); while (!isfib(k), k++); k;

%o prevfib(n) = my(k=n-1); while (!isfib(k), k--); k;

%o a(n) = sum(k=1, n, prevfib(k) + nextfib(k) - 2*k); \\ _Michel Marcus_, Apr 10 2020

%Y Cf. A000045, A001076, A087172, A130473, A194029, A256654, A280514.

%K nonn

%O 1,5

%A _Ctibor O. Zizka_, Apr 09 2020