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A079028 a(0) = 1, a(n) = (n+4)*4^(n-1) for n >= 1. 6
1, 5, 24, 112, 512, 2304, 10240, 45056, 196608, 851968, 3670016, 15728640, 67108864, 285212672, 1207959552, 5100273664, 21474836480, 90194313216, 377957122048, 1580547964928, 6597069766656, 27487790694400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

Table of n, a(n) for n=0..21.

F. Disanto, A. Frosini, R. Pinzani and S. Rinaldi, A closed formula for the number of convex permutominoes, arXiv:math/0702550 [math.CO], 2007.

FORMULA

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

a(n) = (1/4)*(n-1)*4^(n-1)+4^(n-1), with n>=1. - Paolo P. Lava, Jul 08 2008

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)

MATHEMATICA

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

PROG

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

CROSSREFS

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

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

Sequence in context: A225116 A296770 A081104 * A218987 A272257 A347029

Adjacent sequences:  A079025 A079026 A079027 * A079029 A079030 A079031

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Feb 01 2003

STATUS

approved

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Last modified June 25 16:08 EDT 2022. Contains 354851 sequences. (Running on oeis4.)