STATUS
proposed
approved
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Revision History for A099922
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
STATUS
editing
proposed
FORMULA
G.f.: x*(1+8x8*x+x^2)/((1-x)^2 * (1-7x7*x+x^2)). [Corrected for offset by Georg Fischer, May 24 2019]
STATUS
reviewed
editing
STATUS
proposed
reviewed
STATUS
editing
proposed
FORMULA
a(n) = Sum[_{k=1..n, } Lucas(2n2k-1)^2 ].
STATUS
proposed
editing
STATUS
editing
proposed
LINKS
Colin Barker, <a href="/A099922/b099922.txt">Table of n, a(n) for n = 1..1000</a>
FORMULA
From Colin Barker, May 25 2019: (Start)
a(n) = (-((7-3*sqrt(5))/2)^n + ((7+3*sqrt(5))/2)^n)/sqrt(5) - 2*n.
a(n) = 9*a(n-1) - 16*a(n-2) + 9*a(n-3) - a(n-4) for n>4.
(End)
PROG
(PARI) Vec(x*(1 + 8*x + x^2) / ((1 - x)^2*(1 - 7*x + x^2)) + O(x^25)) \\ Colin Barker, May 25 2019
STATUS
proposed
editing
STATUS
editing
proposed
NAME
a(n) = F(4n) - 2n, where F(n) = Fibonacci numbers A000045.