A120741 a(n) = (7^n - 1)/2.

0, 3, 24, 171, 1200, 8403, 58824, 411771, 2882400, 20176803, 141237624, 988663371, 6920643600, 48444505203, 339111536424, 2373780754971, 16616465284800, 116315256993603, 814206798955224, 5699447592686571, 39896133148806000

Offset: 0

Author

Gary W. Adamson, Jun 30 2006

Keywords

• nonn
• easy

Comments

Number of compositions of odd natural numbers into n parts < 7. - Adi Dani, Jun 11 2011

Examples

			From _Adi Dani_, Jun 11 2011: (Start)
  a(2)=24: there are 24 compositions of odd numbers into 2 parts < 7:
  1: (0,1), (1,0);
  3: (0,3), (3,0), (1,2), (2,1);
  5: (0,5), (5,0), (1,4), (4,1), (2,3), (3,2);
  7: (1,6), (6,1), (2,5), (5,2), (3,4), (4,3);
  9: (3,6), (6,3), (4,5), (5,4);
  11: (5,6),(6,5).  (End)
a(4) = 1200 = A034494(4) - 1, where A034494(4) = 1201.
a(4) = 1200 = 8*a(3) - 7*a(2) = 8*171 - 7*24.
a(4) = 1200 = right term in M^n * [1,0] = [A034494(4), a(4)] = [1201, 1200].
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Adi Dani, Restricted compositions of natural numbers
• Index entries for linear recurrences with constant coefficients, signature (8,-7).

Crossrefs

Cf. A034494.

Programs

Magma

[(7^n-1)/2: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Mathematica

Table[1/2*(7^n - 1), {n, 0, 25}]

PARI

a(n)=7^n\2 \\ Charles R Greathouse IV, Jun 11 2011

SageMath

[(7^n-1)/2 for n in range(31)] # G. C. Greubel, Nov 11 2022

Formula

a(n) = A034494(n) - 1.

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

a(n) = right term in M^n * [1,0], where M is the 2 X 2 matrix [4,3; 3,4].

From G. C. Greubel, Nov 11 2022: (Start)

G.f.: 3*x/((1-x)*(1-7*x)).

E.g.f.: (1/2)*(exp(7*x) - exp(x)). (End)

Extensions

Complete edit by Joerg Arndt, Jun 11 2011