OFFSET
1,2
COMMENTS
This parallels Cassini's identity for Fibonacci numbers (Mathworld).
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (5,5,-1).
FORMULA
G.f. -x^2*(-5+x) / ( (1+x)*(1-6*x+x^2) ). - R. J. Mathar, Sep 21 2011
From Colin Barker, Nov 04 2016: (Start)
a(n) = (6*(-1)^n+(3-2*sqrt(2))^n+(3+2*sqrt(2))^n)/8 for n>0.
a(n) = 5*a(n-1)+5*a(n-2)-a(n-3) for n>3.
(End)
EXAMPLE
a(5) = P(4)*P(6) = 12*70 = 840 = P(5)-1 = 29^2-1.
PROG
(PARI) concat(0, Vec(-x^2*(-5+x)/((1+x)*(1-6*x+x^2)) + O(x^30))) \\ Colin Barker, Nov 04 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jeremy C. Buchanan (jbuchanan(AT)myhww.org), Nov 21 2005
STATUS
approved