OFFSET
0,2
COMMENTS
n-th difference of a(n), a(n-1), ..., a(0) is A000420(n-1) for n >= 1.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (9,-8).
FORMULA
a(n) = (8^n + 6)/7. - Ralf Stephan, Feb 14 2004
From Philippe Deléham, Oct 05 2009: (Start)
a(0)=1, a(1)=2; a(n) = 9*a(n-1) - 8*a(n-2) for n>1.
G.f.: (1 - 7*x)/(1 - 9*x + 8*x^2). (End)
a(n) = 8*a(n-1) - 6 for n>0, a(0)=1. - Vincenzo Librandi, Aug 06 2010
a(n+1) = A226308(3*n). - Philippe Deléham, Feb 24 2014
E.g.f.: exp(x)*(6 + exp(7*x))/7. - Stefano Spezia, Oct 16 2023
MAPLE
a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=8*a[n-1]+1 od: seq(a[n]+1, n=0..18); # Zerinvary Lajos, Mar 20 2008
MATHEMATICA
LinearRecurrence[{9, -8}, {1, 2}, 30] (* Harvey P. Dale, Dec 11 2016 *)
(8^Range[0, 40] +6)/7 (* G. C. Greubel, Jan 12 2025 *)
PROG
(Magma) [(8^n +6)/7: n in [0..40]]; // G. C. Greubel, Jan 12 2025
(Python)
def A047853(n): return (pow(8, n) +6)//7
print([A047853(n) for n in range(41)]) # G. C. Greubel, Jan 12 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, Nov 07 2008
STATUS
approved