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A179018 Partial sums of ceil(Fibonacci(n)/2) 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums of A173173.

LINKS

Table of n, a(n) for n=0..30.

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)=ceil(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)

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: A060961 A225393 A243850 * A205476 A170805 A013984

Adjacent sequences:  A179015 A179016 A179017 * A179019 A179020 A179021

KEYWORD

nonn,easy

AUTHOR

Mircea Merca, Jan 04 2011

STATUS

approved

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Last modified March 26 04:32 EDT 2019. Contains 321481 sequences. (Running on oeis4.)