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A167032
a(n) = 20*a(n-1) - 64*a(n-2) + 2 for n > 1; a(0) = 1, a(1) = 21.
5
1, 21, 358, 5818, 93450, 1496650, 23952202, 383258442, 6132227914, 98116017994, 1569857773386, 25117730316106, 401883708825418, 6430139436277578, 102882231360724810, 1646115703292731210, 26337851258768236362
OFFSET
0,2
COMMENTS
lim_{n -> infinity} a(n)/a(n-1) = 16.
FORMULA
a(n) = (257*16^n - 85*4^n + 8)/180.
G.f.: (1+x^2)/((1-x)*(1-4*x)*(1-16*x)).
From G. C. Greubel, May 30 2016: (Start)
a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3) for n>2.
E.g.f.: (1/180)*(257*exp(16*x) - 85*exp(4*x) + 8*exp(x)). (End)
MAPLE
A167032:=n->(257*16^n - 85*4^n + 8)/180: seq(A167032(n), n=0..25); # Wesley Ivan Hurt, May 30 2016
MATHEMATICA
LinearRecurrence[{21, -84, 64}, {1, 21, 358}, 50] (* G. C. Greubel, May 30 2016 *)
RecurrenceTable[{a[0]==1, a[1]==21, a[n]==20a[n-1]-64a[n-2]+2}, a, {n, 20}] (* Harvey P. Dale, Oct 27 2019 *)
PROG
(Magma) [ n le 2 select 20*n-19 else 20*Self(n-1)-64*Self(n-2)+2: n in [1..17] ];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Oct 27 2009
STATUS
approved