A229198 Difference between integers nearest to (2^((n-3)/2) + 3^((n-3)/2)) (A229194) and Fibonacci numbers (A000045).

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 8, 19, 42, 89, 183, 366, 718, 1385, 2636, 4961, 9249, 17105, 31416, 57356, 104170, 188331, 339119, 608464, 1088286, 1940994, 3453084, 6129207, 10857097, 19196490, 33884792, 59721438, 105113418, 184774518, 324436647, 569068543, 997205614, 1745923072, 3054338540, 5339361915, 9327547185, 16284517131, 28414038840, 49551994304, 86372825386, 150486363173

Offset: 0

Author

Vladimir Pletser, Sep 15 2013

Keywords

• nonn

Comments

The following terms are Fibonacci numbers: a(9) = F(2), a(10)= F(4) , a(11) = F(6), a(14) = F(11); or the algebraic sum of two Fibonacci numbers: a(12) = F(8) - F(3), a(13) = F(10) - F(7), a(14) = F(12) - F(10); or the algebraic sum of three Fibonacci numbers: a(15) = F(12) + F(9) + F(5), a(16) = F(14) - F(6) - F(4), a(18) = F(16) + F(14) + F(8), a(19) = F(18) + F(10) - F(3).

Links

• Vladimir Pletser, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000045, A229194.

Programs

Maple

with (combinat): seq(round(2^((n-3)/2)+3^((n-3)/2))-fibonacci(n), n=0..50);

Formula

a(n) = A229194(n) - A000045(n)