OFFSET
0,2
COMMENTS
Also the number of strings of length n with the digits 2 and 3 with the property that the sum of the digits of all substrings of uneven length is not divisible by 5. An example with length 8 is 32332333 . - Herbert Kociemba, Apr 29 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,4,-3,-3).
FORMULA
a(n) = a(n-1) + 4*a(n-2) - 3*a(n-3) - 3*a(n-4).
a(0) = 1; for n>0 odd, a(n) = 7 * 3^floor(n/2) - F(n+4); for n>0 even, a(n) = 4 * 3^floor(n/2) - F(n+4) where F(n) is the n-th Fibonacci number. - Barry Guiduli (guiduli(AT)gmail.com), Jun 23 2005
G.f.: (1+x-2x^2-x^3+x^4) / ((1-x-x^2)(1-3x^2)). - David Callan, Jul 22 2008
MATHEMATICA
Join[{1}, LinearRecurrence[{1, 4, -3, -3}, {2, 4, 8, 16}, 30]] (* Vincenzo Librandi, Apr 30 2017 *)
PROG
(Magma) I:=[2, 4, 8, 16]; [1] cat [n le 4 select I[n] else Self(n-1)+4*Self(n-2)-3*Self(n-3)-3*Self(n-4): n in [1..40]]; // Vincenzo Librandi, Apr 30 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved