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A125831 a(n) = (5^n - 1)/2. 8
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 (list; graph; refs; listen; history; text; internal format)
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
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
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

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Last modified June 13 23:50 EDT 2024. Contains 373391 sequences. (Running on oeis4.)