A048501 a(n) = 2^(n-1)*(8*n-14) + 8.

1, 2, 12, 48, 152, 424, 1096, 2696, 6408, 14856, 33800, 75784, 167944, 368648, 802824, 1736712, 3735560, 7995400, 17039368, 36175880, 76546056, 161480712, 339738632, 713031688, 1493172232, 3120562184, 6509559816, 13555990536, 28185722888, 58518929416

Offset

0,2

Comments

Original name: a(n) = T(7,n), array T given by A048494.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Formula

G.f.: (1-3*x+10*x^2)/((1-x)*(1-2*x)^2). - Colin Barker, Aug 24 2016

From Elmo R. Oliveira, Oct 31 2025: (Start)

E.g.f.: exp(x)*(8 + exp(x)*(8*x - 7)).

a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). (End)

Mathematica

Table[2^(n-1) (8n-14)+8, {n, 0, 30}] (* or *) LinearRecurrence[{5, -8, 4}, {1, 2, 12}, 30] (* Harvey P. Dale, Nov 22 2014 *)

Prog

(Magma) [2^(n-1)*(8*n-14)+8 : n in [0..30]]; // Vincenzo Librandi, Sep 25 2011
(PARI) Vec((1-3*x+10*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ Colin Barker, Aug 24 2016

Crossrefs

Cf. A048494.

Sequence in context: A069946 A176684 A216152 * A001815 A347324 A333728

Adjacent sequences: A048498 A048499 A048500 * A048502 A048503 A048504

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

Formula from Ralf Stephan, Jan 15 2004

Status

approved