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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 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

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