A097162 a(n) = Sum_{k=0..n} C(floor((n+1)/2),floor((k+1)/2))*2^k.

1, 3, 7, 21, 37, 123, 187, 681, 937, 3663, 4687, 19341, 23437, 100803, 117187, 520401, 585937, 2667543, 2929687, 13599861, 14648437, 69047883, 73242187, 349433721, 366210937, 1763945823, 1831054687, 8886837981, 9155273437, 44702625363

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,9,-9,-20,20)

Formula

G.f.: (1+2*x-5*x^2-4*x^3)/((1-x)*(1-4*x^2)*(1-5*x^2)).

a(n) = (3/4-3*sqrt(5)/4)*(-sqrt(5))^n +(3/4+3*sqrt(5)/4)*(sqrt(5))^n-(2^n-(-2)^n)-1/2.

a(2*n) = A057651(n); a(2*n+1)=3*A097165(n).

a(n+5) = 20*a(n)-20*a(n+1)-9*a(n+2)+9*a(n+3)+a(n+4). - Robert Israel, Sep 18 2014

Maple

A097162:=n->add(binomial(floor((n+1)/2), floor((k+1)/2))*2^k, k=0..n): seq(A097162(n), n=0..30); # Wesley Ivan Hurt, Sep 18 2014

Mathematica

LinearRecurrence[{1, 9, -9, -20, 20}, {1, 3, 7, 21, 37}, 50] (* Vincenzo Librandi, Jan 30 2012 *)

Crossrefs

Cf. A075427.

Cf. A057651, A097165.

Sequence in context: A046528 A018572 A018641 * A128402 A018689 A119959

Adjacent sequences: A097159 A097160 A097161 * A097163 A097164 A097165

Keyword

easy,nonn

Author

Paul Barry, Jul 30 2004

Status

approved