OFFSET
1,2
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (7,0,1,-7).
FORMULA
a(n) = 7*a(n-1) + a(n-3) - 7*a(n-4).
G.f.: x*(1 + x^2)/((1 - x)*(1 - 7*x)*(1 + x + x^2)). - Colin Barker, Dec 24 2015
From Stefano Spezia, Mar 31 2023: (Start)
E.g.f.: exp(-x/2)*(exp(3*x/2)*(25*exp(6*x) - 19) - 6*cos(sqrt(3)*x/2) + 8*sqrt(3)*sin(sqrt(3)*x/2))/171.
a(n) ~ 25*7^n/171. (End)
MATHEMATICA
Table[FromDigits[PadRight[{}, n, {1, 0, 1}], 7], {n, 30}] (* or *) LinearRecurrence[ {7, 0, 1, -7}, {1, 7, 50, 351}, 30] (* Harvey P. Dale, Feb 04 2019 *)
PROG
(PARI) Vec(x*(1+x^2)/((1-x)*(1-7*x)*(1+x+x^2)) + O(x^30)) \\ Colin Barker, Dec 24 2015
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved