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A083076
Third row of number array A083075.
7
1, 5, 33, 229, 1601, 11205, 78433, 549029, 3843201, 26902405, 188316833, 1318217829, 9227524801, 64592673605, 452148715233, 3165041006629, 22155287046401, 155087009324805, 1085609065273633, 7599263456915429, 53194844198408001
OFFSET
0,2
COMMENTS
Binomial transform of A067411. Inverse binomial transform of A082412.
Trinomial transform of Jacobsthal numbers A001045. - Paul Barry, Sep 10 2007
FORMULA
a(n) = (2*7^n + 1)/3.
G.f.: (1-3*x)/((1-x)*(1-7*x)).
E.g.f.: (2*exp(7*x) + exp(x))/3.
a(n) = Sum_{k=0..2*n} trinomial(n,k)*Fibonacci(k+1), where trinomial(n,k) are the trinomial coefficients (A027907). - Paul Barry, Sep 10 2007
a(n) = 7*a(n-1) - 2, a(n) = 8*a(n-1) - 7*a(n-2). - Vincenzo Librandi, Nov 06 2011
MAPLE
seq((2*7^n+1)/3, n=0..20); # Nathaniel Johnston, Jun 26 2011
PROG
(Magma) [(2*7^n+1)/3: n in [0..30]]; // Vincenzo Librandi, Nov 06 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Apr 23 2003
STATUS
approved