A081625 a(n) = 2*5^n - 3^n.

1, 7, 41, 223, 1169, 6007, 30521, 154063, 774689, 3886567, 19472201, 97479103, 487749809, 2439811927, 12202248281, 61020807343, 305132734529, 1525749766087, 7629007110761, 38145810394783, 190731376496849

Offset: 0

Author

Paul Barry, Mar 25 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A016516. Inverse binomial transform of A081626.

Row sums of the triangle of 2^n terms shown in A178590 appears to = A081625. - Gary W. Adamson, May 29 2010

Binomial transform of A006516: (1, 6, 28, 120, 496, ...). - Gary W. Adamson, May 31 2010

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-15).

Crossrefs

Cf. A178590, A006516.

Programs

Magma

[2*5^n-3^n: n in [0..25]]; // Vincenzo Librandi, Aug 09 2013

Mathematica

CoefficientList[Series[(1 - x) / ((1 - 3 x) (1 - 5 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 09 2013 *)
LinearRecurrence[{8,-15},{1,7},30] (* Harvey P. Dale, Oct 14 2013 *)

Formula

a(n) = 8*a(n-1) - 15*a(n-2), a(0)=1, a(1)=7.

G.f.: (1-x)/((1-3*x)(1-5*x)).

E.g.f. 2*exp(5*x) - exp(3*x).

a(n) = Sum_{k=0..n} A125185(n,k)*3^k. - Philippe Deléham, Feb 26 2012