A088795 - OEIS

A088795

a(n) = -1/16-3*n^2/8+17*n/12+n^3/12+(-1)^n/16.

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, 9550

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OFFSET

1,2

COMMENTS

Previous name was: Fibonacci(n) as n runs through the quarter-squares. [this is misleading]

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..50.

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

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. - 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.