OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (10,-23,14).
FORMULA
a(n) = (49*7^n - 24*2^n + 5)/30. - Bruno Berselli, Feb 09 2011
a(0)=1, a(n) = 7*a(n-1) + 2^(n+1) - 1. - Vincenzo Librandi, Feb 09 2011
From Elmo R. Oliveira, Mar 27 2025: (Start)
E.g.f.: exp(x)*(49*exp(6*x) - 24*exp(x) + 5)/30.
a(n) = 10*a(n-1) - 23*a(n-2) + 14*a(n-3).
MAPLE
a:=n->sum((7^(n-j+1)-2^(n-j+1))/5, j=0..n+1): seq(a(n), n=0..19); # Zerinvary Lajos, Jan 15 2007
MATHEMATICA
CoefficientList[Series[1/((1-x)(1-2x)(1-7x)), {x, 0, 20}], x](* or *) LinearRecurrence[{10, -23, 14}, {1, 10, 77}, 20] (* Harvey P. Dale, Mar 06 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Elmo R. Oliveira, Mar 27 2025
STATUS
approved