OFFSET
2,2
COMMENTS
An integral pentagon is a pentagon with integer sides and diagonals. There are two types of such pentagons. Type A have sides A066259(n+1), A220360(n+1), A066259(n+1), A220360(n+1), A066259(n+1), and opposite diagonals A056570(n+2), A056570(n+2), A220361(n+2), A056570(n+2), A056570(n+2), for n=1,2,...
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, D20.
LINKS
Indranil Ghosh, Table of n, a(n) for n = 2..1593
J. H. Jordan, B. E. Peterson, Almost regular integer Fibonacci pentagons, Rocky Mountain J. Math. Volume 23, Number 1 (1993), 243-247.
Index entries for linear recurrences with constant coefficients, signature (3,6,-3,-1).
FORMULA
a(n) = 3*a(n-1)+6*a(n-2)-3*a(n-3)-a(n-4). G.f.: x^2*(x^2+4*x+1) / ((x^2-x-1)*(x^2+4*x-1)). - Colin Barker, Sep 23 2014
MAPLE
with(combinat): A220361:=n->fibonacci(n)^3+(-1)^n*fibonacci(n-2): seq(A220361(n), n=2..30); # Wesley Ivan Hurt, Apr 26 2017
MATHEMATICA
Table[Fibonacci[n]^3 + (-1)^n * Fibonacci[n - 2], {n, 2, 30}] (* T. D. Noe, Dec 13 2012 *)
LinearRecurrence[{3, 6, -3, -1}, {1, 7, 28, 123}, 30] (* Harvey P. Dale, Jul 13 2021 *)
PROG
(PARI) Vec(x^2*(x^2+4*x+1)/((x^2-x-1)*(x^2+4*x-1)) + O(x^100)) \\ Colin Barker, Sep 23 2014
(PARI) a(n) = fibonacci(n)^3 + (-1)^n*fibonacci(n-2) \\ Charles R Greathouse IV, Feb 14 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michel Marcus, Dec 12 2012
STATUS
approved