A191821 a(n) = n*(2^n - n + 1) + 2^(n-1)*(n^2 - 3*n + 2).

2, 6, 26, 100, 332, 994, 2774, 7368, 18872, 47014, 114578, 274300, 647012, 1507146, 3473198, 7929616, 17956592, 40369870, 90177194, 200277636, 442498652, 973078066, 2130705926, 4647288280, 10099883432, 21877489014, 47244639554, 101737037068

Offset

1,1

Comments

Conjecture: generating function = -((2 (-1+6 x-19 x^2+31 x^3-22 x^4+4 x^5))/(1-3 x+2 x^2)^3) - Harvey P. Dale, May 10 2021

Links

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

Index entries for linear recurrences with constant coefficients, signature (9,-33,63,-66,36,-8).

Formula

G.f.: -2*x*(-1 + 6*x - 19*x^2 + 31*x^3 - 22*x^4 + 4*x^5) / ( (2*x-1)^3*(x-1)^3 ). - R. J. Mathar, Aug 26 2011

Mathematica

LinearRecurrence[{9, -33, 63, -66, 36, -8}, {2, 6, 26, 100, 332, 994}, 50] (* Vincenzo Librandi, Nov 25 2011 *)
Table[n(2^n-n+1)+2^(n-1) (n^2-3n+2), {n, 30}] (* Harvey P. Dale, May 10 2021 *)

Prog

(PARI) a(n)=(n^2-n+2)<<(n-1)-n*(n-1) \\ Charles R Greathouse IV, Jul 13 2011
(Magma) [n*(2^n-n+1)+2^(n-1)*(n^2-3*n+2): n in [1..40]]; // Vincenzo Librandi, Nov 25 2011

Crossrefs

Cf. A188377, A188947, A189890.

Sequence in context: A027231 A083845 A027239 * A290958 A323265 A285024

Adjacent sequences: A191818 A191819 A191820 * A191822 A191823 A191824

Keyword

nonn,easy

Author

Adeniji, Adenike, Jun 17 2011

Status

approved