A179053 Partial sums of ceiling(Fibonacci(n)/11).

0, 1, 2, 3, 4, 5, 6, 8, 10, 14, 19, 28, 42, 64, 99, 155, 245, 391, 626, 1007, 1622, 2618, 4229, 6835, 11051, 17872, 28908, 46765, 75657, 122406, 198046, 320435, 518464, 838881, 1357326, 2196187, 3553492, 5749658

Offset

0,3

Links

Table of n, a(n) for n=0..37.

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

Formula

a(n) = round(Fibonacci(n+2)/11 + 3*n/5 + 43/110).

a(n) = floor(Fibonacci(n+2)/11 + 3*n/5 + 48/55).

a(n) = ceiling(Fibonacci(n+2)/11 + 3*n/5 - 1/11).

a(n) = a(n-10) + Fibonacci(n-3) + 6, n > 9.

a(n) = 2*a(n-1) - a(n-3) + a(n-10) - 2*a(n-11) + a(n-13), n > 12.

G.f.: x*(-1 + x^2 + x^3 + x^4 + x^5 + x^7 + x^9 + x^10) / ( (1+x)*(x^2 + x - 1)*(x^4 + x^3 + x^2 + x + 1)*(x^4 - x^3 + x^2 - x + 1)*(x-1)^2 ).

Example

a(11) = 0 + 1 + 1 + 1 + 1 + 1 + 1 + 2 + 2 + 4 + 5 + 9 = 28.

Maple

A179053 := proc(n) add( ceil(combinat[fibonacci](i)/11) , i=0..n) ; end proc:

Crossrefs

Sequence in context: A276642 A320317 A017846 * A218949 A129976 A105181

Adjacent sequences: A179050 A179051 A179052 * A179054 A179055 A179056

Keyword

nonn

Author

Mircea Merca, Jan 04 2011

Status

approved