A147296 a(n) = n*(9*n+2).

0, 11, 40, 87, 152, 235, 336, 455, 592, 747, 920, 1111, 1320, 1547, 1792, 2055, 2336, 2635, 2952, 3287, 3640, 4011, 4400, 4807, 5232, 5675, 6136, 6615, 7112, 7627, 8160, 8711, 9280, 9867, 10472, 11095, 11736, 12395, 13072, 13767, 14480, 15211, 15960

Offset

0,2

Comments

For n >= 1, the continued fraction expansion of sqrt(4*a(n)) is [6n; {1, 1, 1, 3n-1, 1, 1, 1, 12n}]. - Magus K. Chu, Sep 17 2022

Links

Table of n, a(n) for n=0..42.

Reply to V. Librandi, A147296 (SeqFan list). - M. F. Hasler, Mar 01 2009

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = n*(9*n + 2), as conjectured by V. Librandi. - M. F. Hasler, Mar 01 2009

G.f.: x*(11+7*x)/(1-x)^3. - Jaume Oliver Lafont, Aug 30 2009

a(n) = floor((3*n + 1/3)^2). - Reinhard Zumkeller, Apr 14 2010

From Elmo R. Oliveira, Dec 15 2024: (Start)

E.g.f.: exp(x)*x*(11 + 9*x).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. (End)

Mathematica

Table[n(9n+2), {n, 0, 50}] (* Harvey P. Dale, Dec 19 2014 *)
(* Alternative: *)
LinearRecurrence[{3, -3, 1}, {0, 11, 40}, 50] (* Harvey P. Dale, Dec 19 2014 *)

Prog

(PARI) A147296(n) = n*(9*n + 2) \\ M. F. Hasler, Mar 01 2009

Crossrefs

Equals first 9-fold decimation of A144454.

Cf. A010701, A017173, A147296, A185019.

Sequence in context: A342833 A335491 A031427 * A337130 A353447 A059142

Adjacent sequences: A147293 A147294 A147295 * A147297 A147298 A147299

Keyword

nonn,easy

Author

Paul Curtz, Nov 05 2008

Extensions

More terms from M. F. Hasler, Mar 01 2009

Status

approved