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

Author

Paul Barry, Apr 23 2003

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A034478, A066443, A082761, A083077.

Programs

Magma

[(2*7^n+1)/3: n in [0..30]]; // Vincenzo Librandi, Nov 06 2011

Maple

seq((2*7^n+1)/3,n=0..20); # Nathaniel Johnston, Jun 26 2011

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