OFFSET
3,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 3..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
Numerators of sequence a[ n, n-2 ] in (a[ i, j ])^3 where a[ i, j ] = binomial(i-1, j-1)/2^(i-1) if j <= i, 0 if j > i.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(3)=49, a(4)=147, a(5)=294. - Harvey P. Dale, Aug 24 2011
G.f.: 49*x^3/(1-x)^3. - Harvey P. Dale, Aug 24 2011
From Amiram Eldar, Sep 04 2022: (Start)
a(n) = A162942(n-2).
Sum_{n>=3} 1/a(n) = 2/49.
Sum_{n>=3} (-1)^(n+1)/a(n) = 2*(2*log(2)-1)/49. (End)
MATHEMATICA
Table[49(n-1)(n-2)/2, {n, 3, 70}] (* or *) LinearRecurrence[{3, -3, 1}, {49, 147, 294}, 70] (* Harvey P. Dale, Aug 24 2011 *)
PROG
(Magma) [49*(n-1)*(n-2)/2: n in [3..50]]; // Vincenzo Librandi, Aug 25 2011
(PARI) a(n)=49*(n-1)*(n-2)/2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Harvey P. Dale, Aug 24 2011
STATUS
approved