A079028 a(0) = 1, a(n) = (n + 4)*4^(n-1) for n >= 1.

1, 5, 24, 112, 512, 2304, 10240, 45056, 196608, 851968, 3670016, 15728640, 67108864, 285212672, 1207959552, 5100273664, 21474836480, 90194313216, 377957122048, 1580547964928, 6597069766656, 27487790694400, 114349209288704, 474989023199232, 1970324836974592, 8162774324609024

Offset: 0

Author

Benoit Cloitre, Feb 01 2003

Keywords

• nonn
• easy

Comments

a(n) = det(M(n)) where M(n) is the n X n matrix defined by m(i,i) = 5, m(i,j) = i/j.

Main diagonal of array defined by m(1,j) = j; m(i,1) = i and m(i,j) = m(i-1,j) + 3*m(i-1,j-1).

4th binomial transform of (1,1,0,0,0,0,...). - Paul Barry, Mar 07 2003

Number of independent vertex subsets of the graph obtained by attaching two pendant edges to each vertex of the complete graph K_n (see A235113). Example: a(1)=5; indeed, K_1 is the one vertex graph and after attaching two pendant vertices we obtain the path graph ABC; the independent vertex subsets are: empty, {A}, {B}, {C}, and {A,C}. - Emeric Deutsch, Jan 13 2014

Row sums of A235113.

Links

• F. Disanto, A. Frosini, R. Pinzani and S. Rinaldi, A closed formula for the number of convex permutominoes, arXiv:math/0702550 [math.CO], 2007.
• Index entries for linear recurrences with constant coefficients, signature (8,-16).

Crossrefs

Cf. A001792, A006234, A081105, A006234, A235113.

Cf. A002697, A034007, A079861, A045891, A087449.

Programs

Mathematica

LinearRecurrence[{8, -16}, {1, 5}, 22] (* Jean-François Alcover, Nov 06 2018 *)

Sage

[lucas_number2(n, 4, 0)*n/2^10 for n in range(4, 26)] # Zerinvary Lajos, Mar 13 2009

Formula

a(n) = 8*a(n-1)-16*a(n-2), a(0) = 1, a(1) = 5. - Paul Barry, Mar 07 2003

G.f.: (1 - 3*x)/(1 - 4*x)^2. - Philippe Deléham, Dec 11 2008

From Amiram Eldar, Jan 14 2021: (Start)

Sum_{n>=0} 1/a(n) = 1024*log(4/3) - 880/3.

Sum_{n>=0} (-1)^n/a(n) = 688/3 - 1024*log(5/4). (End)

E.g.f.: exp(4*x)*(1 + x). - Stefano Spezia, Mar 05 2023

Extensions

More terms from Stefano Spezia, Mar 05 2023