A179018 Partial sums of ceiling(Fibonacci(n)/2).

0, 1, 2, 3, 5, 8, 12, 19, 30, 47, 75, 120, 192, 309, 498, 803, 1297, 2096, 3388, 5479, 8862, 14335, 23191, 37520, 60704, 98217, 158914, 257123, 416029, 673144, 1089164, 1762299, 2851454, 4613743, 7465187, 12078920, 19544096, 31623005, 51167090, 82790083, 133957161

Offset

0,3

Comments

Partial sums of A173173.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

Index entries for linear recurrences with constant coefficients, signature (2,0,0,-2,0,1).

Formula

a(n) = round(Fibonacci(n+2)/2 + (n-1)/3).

a(n) = round(Fibonacci(n+2)/2 + n/3 - 1/2).

a(n) = floor(Fibonacci(n+2)/2 + n/3 - 1/6).

a(n) = ceiling(Fibonacci(n+2)/2 + n/3 - 1/2).

a(n) = a(n-3) + Fibonacci(n)+1, n > 2.

a(n) = 2*a(n-1) - 2*a(n-4) + a(n-6), n > 5.

G.f.: x*(x^3+x^2-1) / ( (x^2+x+1)*(x^2+x-1)*(x-1)^2 ).

Example

a(4) = 0 + 1 + 1 + 1 + 2 = 5.

Maple

seq(ceil(Fibonacci(n+2)/2+n/3-1/2), n=0..30)

Mathematica

Accumulate[Ceiling[Fibonacci[Range[0, 50]]/2]] (* Paolo Xausa, Nov 07 2025 *)
LinearRecurrence[{2, 0, 0, -2, 0, 1}, {0, 1, 2, 3, 5, 8}, 50] (* Harvey P. Dale, Feb 05 2026 *)

Prog

(PARI) a(n)=(3*fibonacci(n+2)+2*n-1)\6 \\ Charles R Greathouse IV, Nov 02 2015

Crossrefs

Cf. A173173.

Sequence in context: A225393 A243850 A357519 * A352476 A205476 A170805

Adjacent sequences: A179015 A179016 A179017 * A179019 A179020 A179021

Keyword

nonn,easy

Author

Mircea Merca, Jan 04 2011

Extensions

a(31) onward from Andrew Howroyd, Nov 07 2025

Status

approved