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A027004
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a(n) = T(2*n+1,n+1), T given by A026998.
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1
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1, 8, 26, 73, 196, 518, 1361, 3568, 9346, 24473, 64076, 167758, 439201, 1149848, 3010346, 7881193, 20633236, 54018518, 141422321, 370248448, 969323026, 2537720633, 6643838876, 17393795998, 45537549121, 119218851368, 312119004986, 817138163593, 2139295485796
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-4,1).
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FORMULA
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a(n) = Fibonacci(2*n+3) + 2*Fibonacci(2*n+2) - 3.
From Colin Barker, Feb 18 2016: (Start)
a(n) = 2^(-n)*(-3*2^n-(3-sqrt(5))^n*(-2+sqrt(5))+(2+sqrt(5))*(3+sqrt(5))^n).
a(n) = 4*a(n-1)-4*a(n-2)+a(n-3) for n>2.
G.f.: (1+4*x-2*x^2) / ((1-x)*(1-3*x+x^2)).
(End)
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PROG
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(MAGMA) [Fibonacci(2*n+3) + 2*Fibonacci(2*n+2) - 3: n in [0..30]]; // Vincenzo Librandi, Apr 18 2011
(PARI) Vec((1+4*x-2*x^2)/((1-x)*(1-3*x+x^2)) + O(x^40)) \\ Colin Barker, Feb 18 2016
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CROSSREFS
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A002878(n+1) - 3.
Sequence in context: A296112 A051669 A207101 * A194021 A245126 A278769
Adjacent sequences: A027001 A027002 A027003 * A027005 A027006 A027007
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling
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STATUS
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approved
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