OFFSET
0,2
REFERENCES
Nick Baxter, The Burnside di-lemma: combinatorics and puzzle symmetry, in Tribute to a Mathemagician, Peters, 2005, pp. 199-210.
De Bruijn, Polya's theory of counting, in Beckenbach, ed., Applied Combinatorial Math., Wiley, 1964 (p. 182).
LINKS
Colin Barker, Table of n, a(n) for n = 0..950
Index entries for linear recurrences with constant coefficients, signature (15,-45,-75,250).
FORMULA
a(n+1) = (1/10)*{10^n - 5^n + (4-(-1)^n)*5^[n/2]} (De Bruijn)
From Colin Barker, Jul 03 2017: (Start)
G.f.: (1 - 6*x + 75*x^3) / ((1 - 5*x)*(1 - 10*x)*(1 - 5*x^2)).
a(n) = 5^((n-1)/2+1/2)/2 - 5^n/2 + 10^n for n even.
a(n) = 3*5^((n-1)/2)/2 - 5^n/2 + 10^n for n odd.
a(n) = 15*a(n-1) - 45*a(n-2) - 75*a(n-3) + 250*a(n-4) for n>3.
(End)
MAPLE
f:=n-> if n mod 2 = 0 then 10^n-(5^n-5^(n/2))/2 else 10^n-(5^n-3*5^((n-1)/2))/2; fi;
MATHEMATICA
LinearRecurrence[{15, -45, -75, 250}, {1, 9, 90, 945}, 30] (* Harvey P. Dale, Jul 05 2023 *)
PROG
(PARI) Vec((1 - 6*x + 75*x^3) / ((1 - 5*x)*(1 - 10*x)*(1 - 5*x^2)) + O(x^30)) \\ Colin Barker, Jul 03 2017
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
STATUS
approved