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A088795 Fibonacci(n) as n runs through the quarter-squares. 0
1, 2, 3, 5, 8, 13, 20, 30, 43, 60, 81, 107, 138, 175, 218, 268, 325, 390, 463, 545, 636, 737, 848, 970, 1103, 1248, 1405, 1575, 1758, 1955, 2166, 2392, 2633, 2890, 3163, 3453, 3760, 4085, 4428, 4790, 5171, 5572, 5993, 6435, 6898, 7383, 7890, 8420, 8973 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This recurrence arose when a middle schooler was asked to complete a number sequence, given six of the Fibonacci numbers (1,2,3,5,8,13) but not told about the Fibonacci sequence.

LINKS

Table of n, a(n) for n=1..49.

FORMULA

a(n) = a(n-1) + 1 + A002620(n-2). For n<2: a(1)=1, a(2)=2. O.g.f.: x*(2*x^3-x^2-x+1)/((-1+x)^4*(x+1)). - R. J. Mathar, Dec 05 2007

a(n)=-1/16-3*n^2/8+17*n/12+n^3/12+(-1)^n/16. [From R. J. Mathar, Jul 22 2009]

EXAMPLE

a(3) = a(2) + 1 + A002620(1) = 2+1+0 = 3

a(4) = a(3) + 1 + A002620(2) = 3+1+1 = 5

a(12) = a(11) + 1 + A002620(10) = 81+1+25 = 107.

CROSSREFS

Cf. A002620.

Sequence in context: A045842 A324741 A200462 * A156145 A216053 A173597

Adjacent sequences:  A088792 A088793 A088794 * A088796 A088797 A088798

KEYWORD

nonn

AUTHOR

Stewart Charles Cureton (sarah.cureton(AT)att.net), Oct 16 2003

STATUS

approved

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Last modified August 24 16:10 EDT 2019. Contains 326295 sequences. (Running on oeis4.)