A048468 a(n) = T(7,n), array T given by A047858.

1, 9, 26, 62, 138, 298, 634, 1338, 2810, 5882, 12282, 25594, 53242, 110586, 229370, 475130, 983034, 2031610, 4194298, 8650746, 17825786, 36700154, 75497466, 155189242, 318767098, 654311418, 1342177274, 2751463418, 5637144570, 11542724602, 23622320122, 48318382074

Offset

0,2

Comments

n-th difference of a(n), a(n-1), ..., a(0) is (8, 9, 10, ...).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..3000

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

Formula

From Vincenzo Librandi, Sep 28 2011: (Start)

a(n) = 2^(n-1)*(n+14) - 6.

a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3), a(0)=1, a(1)=9, a(2)=26. (End)

G.f.: (1+4*x-11*x^2)/((1-x)*(1-2*x)^2). - Colin Barker, Feb 18 2016

E.g.f.: exp(x)*(exp(x)*(7 + x) - 6). - Elmo R. Oliveira, Oct 29 2025

Mathematica

LinearRecurrence[{5, -8, 4}, {1, 9, 26}, 30] (* Harvey P. Dale, Apr 19 2012 *)

Prog

(Magma) [2^(n-1)*(n+14)-6: n in [0..30]]; // Vincenzo Librandi, Sep 28 2011
(PARI) Vec((1+4*x-11*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ Colin Barker, Feb 18 2016

Crossrefs

Cf. A047858.

Sequence in context: A338548 A249275 A270695 * A255108 A048771 A055849

Adjacent sequences: A048465 A048466 A048467 * A048469 A048470 A048471

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved