A083076 Third row of number array A083075.

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

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..250

Index entries for linear recurrences with constant coefficients, signature (8,-7).

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

Cf. A034478, A066443, A082761, A083077.

Sequence in context: A164538 A197533 A221441 * A361237 A162816 A128418

Adjacent sequences: A083073 A083074 A083075 * A083077 A083078 A083079

Keyword

nonn,easy

Author

Paul Barry, Apr 23 2003

Status

approved