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A171478
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a(n) = 6*a(n-1) - 8*a(n-2) + 2 for n > 1; a(0) = 1, a(1) = 8.
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2
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1, 8, 42, 190, 806, 3318, 13462, 54230, 217686, 872278, 3492182, 13974870, 55911766, 223671638, 894735702, 3579041110, 14316361046, 57265837398, 229064136022, 916258116950, 3665035613526, 14660148745558, 58640607565142
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OFFSET
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0,2
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COMMENTS
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Second binomial transform of A168648.
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LINKS
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FORMULA
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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
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(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}
(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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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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