A027469 a(n) = 49*(n-1)*(n-2)/2.

49, 147, 294, 490, 735, 1029, 1372, 1764, 2205, 2695, 3234, 3822, 4459, 5145, 5880, 6664, 7497, 8379, 9310, 10290, 11319, 12397, 13524, 14700, 15925, 17199, 18522, 19894, 21315, 22785, 24304, 25872, 27489, 29155, 30870, 32634, 34447, 36309, 38220, 40180

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

Third diagonal of A027466.

Cf. A162942.

Sequence in context: A088535 A045897 A162942 * A044381 A044762 A159247

Adjacent sequences: A027466 A027467 A027468 * A027470 A027471 A027472

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

More terms from Harvey P. Dale, Aug 24 2011

Status

approved