A171478 a(n) = 6*a(n-1) - 8*a(n-2) + 2 for n > 1; a(0) = 1, a(1) = 8.
1, 8, 42, 190, 806, 3318, 13462, 54230, 217686, 872278, 3492182, 13974870, 55911766, 223671638, 894735702, 3579041110, 14316361046, 57265837398, 229064136022, 916258116950, 3665035613526, 14660148745558, 58640607565142
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000 (extending prior file from Vincenzo Librandi)
- Index entries for linear recurrences with constant coefficients, signature (7,-14,8).
Crossrefs
Programs
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GAP
a:=[1,8];; for n in [3..25] do a[n]:=6*a[n-1]-8*a[n-2]+2; od; a; # Muniru A Asiru, Mar 22 2018
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Magma
[(10*4^n-9*2^n+2)/3: n in [0..30]]; // Vincenzo Librandi, Jul 18 2011
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Maple
a:= proc(n) option remember: if n = 0 then 1 elif n = 1 then 8 elif n >= 2 then 6*procname(n-1) - 8*procname(n-2) + 2 fi; end: seq(a(n), n = 0..25); # Muniru A Asiru, Mar 22 2018
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Mathematica
RecurrenceTable[{a[0]==1,a[1]==8,a[n]==6a[n-1]-8a[n-2]+2},a,{n,30}] (* or *) LinearRecurrence[{7,-14,8},{1,8,42},30] (* Harvey P. Dale, May 04 2012 *) -
PARI
{m=23; v=concat([1, 8], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]+2); v}
Formula
a(n) = (10*4^n - 9*2^n + 2)/3.
G.f.: (1+x)/((1-x)*(1-2*x)*(1-4*x)).
a(0)=1, a(1)=8, a(2)=42, a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3). - Harvey P. Dale, May 04 2012
a(n) = A203241(n+1) + 2^n*(2^(n+1)-1), n>0. - J. M. Bergot, Mar 21 2018
Comments