OFFSET
1,2
COMMENTS
Number of unit squares at n-th stage = n^2 + (n-1)^2 (A001844).
First differences are in A255840. - Wesley Ivan Hurt, Mar 13 2015
REFERENCES
Anthony Gardiner, "Mathematical Puzzling," Dover Publications, Inc., Mineola, NY., 1987, page 88.
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).
FORMULA
G.f.: x(5x^2+2x+1)/((1-x^2)(1-x)^3).
a(n) = (8*n^3-2*n+3-3*(-1)^n)/12. - Luce ETIENNE, Aug 21 2014
a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5). - Colin Barker, Sep 29 2014
G.f.: x*(5*x^2+2*x+1) / ((x-1)^4*(x+1)). - Colin Barker, Sep 29 2014
MATHEMATICA
Table[(8*n^3 - 2*n + 3 - 3*(-1)^n)/12, {n, 30}] (* Wesley Ivan Hurt, Mar 13 2015 *)
PROG
(PARI) Vec(x*(5*x^2+2*x+1)/((x-1)^4*(x+1)) + O(x^100)) \\ Colin Barker, Sep 29 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert G. Wilson v, Aug 21 2000
EXTENSIONS
More terms from Colin Barker, Sep 29 2014
STATUS
approved