A125831 a(n) = (5^n - 1)/2.

0, 2, 12, 62, 312, 1562, 7812, 39062, 195312, 976562, 4882812, 24414062, 122070312, 610351562, 3051757812, 15258789062, 76293945312, 381469726562, 1907348632812, 9536743164062, 47683715820312, 238418579101562, 1192092895507812, 5960464477539062, 29802322387695312

Offset

0,2

Comments

Number of compositions of odd numbers into n parts < 5. - Adi Dani, Jun 11 2011

Numbers whose base 5 representation is 22222...2 (n times).

References

S. J. Cyvin, B. N. Cyvin, and J. Brunvoll. Enumeration of tree-like octagonal systems: catapolyoctagons, ACH Models in Chem. 134 (1997), pp. 55-70, eqs. (6) and (7) on p. 58.

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 (6,-5).

Formula

a(n) = 5*a(n-1) + 2 for n > 0, a(0)=0. - Vincenzo Librandi, Sep 30 2010

From Colin Barker, May 16 2013: (Start)

a(n) = 6*a(n-1) - 5*a(n-2).

G.f.: 2*x/((1-x)*(1-5*x)). (End)

a(n) = 2*A003463(n). - Joerg Arndt, Aug 03 2019

From Elmo R. Oliveira, Dec 10 2023: (Start)

a(n) = A024049(n)/2.

E.g.f.: (1/2)*(exp(5*x) - exp(x)). (End)

Example

a(2)=12: there are 12 compositions of odd numbers into 2 parts < 5:
1: (0,1),(1,0);
3: (0,3),(3,0),(1,2),(2,1);
5: (1,4),(4,1),(2,3),(3,2);
7: (3,4),(4,3). - Adi Dani, Jun 11 2011

Maple

seq((5^n-1)/2, n=0..30);

Mathematica

Table[(5^n -1)/2, {n, 0, 30}] (* Harvey P. Dale, Dec 03 2010 *)

Prog

(Magma) [(5^n-1)/2: n in [0..30]]; // Vincenzo Librandi, Jun 11 2011
(PARI) a(n)=5^n\2 \\ Charles R Greathouse IV, Jun 11 2011
(Sage) [(5^n-1)/2 for n in (0..30)] # G. C. Greubel, Aug 03 2019
(GAP) List([0..30], n-> (5^n-1)/2); # G. C. Greubel, Aug 03 2019

Crossrefs

Cf. A003463, A024049, A121177 (same with different offset).

Sequence in context: A321277 A187001 A121177 * A289787 A226506 A026076

Adjacent sequences: A125828 A125829 A125830 * A125832 A125833 A125834

Keyword

easy,nonn

Author

Zerinvary Lajos, Feb 03 2007

Extensions

Offset corrected by N. J. A. Sloane, Oct 02 2010

Major edit by Joerg Arndt, Jun 11 2011

Status

approved