OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
G.f.: x^2*(2+3*x+x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011
From Wesley Ivan Hurt, Jun 03 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5.
a(n) = (14*n - 9 - i^(2*n) + (1 - 3*i)*i^(-n) + (1 + 3*i)*i^n)/8 where i = sqrt(-1).
E.g.f.: (4 - 3*sin(x) + cos(x) + (7*x - 4)*sinh(x) + (7*x - 5)*cosh(x))/4. - Ilya Gutkovskiy, Jun 04 2016
MAPLE
A047324:=n->(14*n-9-I^(2*n)+(1-3*I)*I^(-n)+(1+3*I)*I^n)/8: seq(A047324(n), n=1..100); # Wesley Ivan Hurt, Jun 03 2016
MATHEMATICA
Table[(14n - 9 - I^(2n) + (1 - 3 * I) * I^(-n) + (1 + 3 * I) * I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 03 2016 *)
Flatten[Table[7n + {0, 2, 5, 6}, {n, 0, 15}]] (* Alonso del Arte, Jun 04 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 2, 5, 6, 7}, 80] (* Harvey P. Dale, Jan 10 2023 *)
PROG
(Magma) [n : n in [0..150] | n mod 7 in [0, 2, 5, 6]]; // Wesley Ivan Hurt, Jun 03 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved