A226315 a(n) = (n^2/8+3*n/8-2)*2^n + 3.

0, 0, 5, 27, 99, 307, 867, 2307, 5891, 14595, 35331, 83971, 196611, 454659, 1040387, 2359299, 5308419, 11862019, 26345475, 58195971, 127926275, 279969795, 610271235, 1325400067, 2868903939, 6190792707, 13321109507, 28588376067, 61203283971, 130728067075, 278636003331, 592705486851, 1258425417731

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

W. Y. C. Chen, A. Y. L. Dai and R. D. P. Zhou, Ordered Partitions Avoiding a Permutation of Length 3, arXiv preprint arXiv:1304.3187, 2013. See Th. 1.1.

Index entries for linear recurrences with constant coefficients, signature (7,-18,20,-8).

Formula

G.f.: x^3*(5-8*x)/((1-x)*(1-2*x)^3). - Bruno Berselli, Jun 17 2013

Mathematica

Table[(n^2 / 8 + 3 n / 8 - 2) 2^n + 3, {n, 40}] (* or *) CoefficientList[Series[x^2 (5 - 8 x) / ((1 - x) (1 - 2 x)^3), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 18 2013 *)
LinearRecurrence[{7, -18, 20, -8}, {0, 0, 5, 27}, 40] (* Harvey P. Dale, Jul 10 2018 *)

Prog

(Magma) [(n^2/8+3*n/8-2)*2^n+3: n in [1..35]]; // Vincenzo Librandi, Jun 18 2013
(Magma) I:=[0, 0, 5, 27]; [n le 4 select I[n] else 7*Self(n-1)-18*Self(n-2)+20*Self(n-3)-8*Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 18 2013

Crossrefs

Sequence in context: A338996 A349919 A212783 * A201436 A202508 A129868

Adjacent sequences: A226312 A226313 A226314 * A226316 A226317 A226318

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 09 2013

Status

approved