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A333907 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. 0
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, 47, 44, 39, 32, 23, 12, 20, 39, 56, 71, 84, 95, 104, 111, 116, 119, 120, 119, 116, 111, 104, 95, 84, 71, 56, 39, 20, 33, 65, 95, 123, 149, 173, 195, 215, 233, 249, 263, 275 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

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

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

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

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

PROG

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

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

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

a(n) = sum(k=1, n, prevfib(k) + nextfib(k) - 2*k); \\ Michel Marcus, Apr 10 2020

CROSSREFS

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

Sequence in context: A132439 A338902 A116217 * A274486 A227961 A108838

Adjacent sequences:  A333904 A333905 A333906 * A333908 A333909 A333910

KEYWORD

nonn

AUTHOR

Ctibor O. Zizka, Apr 09 2020

STATUS

approved

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Last modified August 10 13:12 EDT 2022. Contains 356039 sequences. (Running on oeis4.)