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A083879
a(0)=1, a(1)=4, a(n) = 8*a(n-1) - 14*a(n-2), n >= 2.
3
1, 4, 18, 88, 452, 2384, 12744, 68576, 370192, 2001472, 10829088, 58612096, 317289536, 1717746944, 9299922048, 50350919168, 272608444672, 1475954689024, 7991119286784, 43265588647936, 234249039168512, 1268274072276992
OFFSET
0,2
COMMENTS
Binomial transform of A083878.
4th binomial transform of A077957. Inverse binomial transform of A083880. - Philippe Deléham, Nov 30 2008
From L. Edson Jeffery, Apr 26 2011: (Start)
Let G be the Gram matrix
G =
(4 1 0 1)
(1 4 1 0)
(0 1 4 -1)
(1 0 -1 4)
of A028997. Then a(n) = (1/4)*Trace(G^n). (End)
FORMULA
a(n) = 2^((n-2)/2)*(2*sqrt(2)-1)^n + 2^((n-2)/2)*(2*sqrt(2)+1)^n;
a(n) = Sum_{k=0..n} C(n, 2k)*5^(n-2k)2^k.
G.f.: (1-4x)/(1-8x+14x^2).
E.g.f.: exp(4x)cosh(x*sqrt(2)).
((4+sqrt(2))^n + (4-sqrt(2))^n)/2. Offset=0. a(3)=88. - Al Hakanson (hawkuu(AT)gmail.com), Oct 15 2008
a(n) = Sum_{k=0..n} A098158(n,k)*2^(3*k-n). - Philippe Deléham, Nov 30 2008
MATHEMATICA
LinearRecurrence[{8, -14}, {1, 4}, 30] (* Harvey P. Dale, May 08 2013 *)
CROSSREFS
Sequence in context: A199309 A083325 A050146 * A363184 A081671 A244785
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 08 2003
STATUS
approved