A048467 a(n) = T(6,n), array T given by A047858.

1, 8, 23, 55, 123, 267, 571, 1211, 2555, 5371, 11259, 23547, 49147, 102395, 212987, 442363, 917499, 1900539, 3932155, 8126459, 16777211, 34603003, 71303163, 146800635, 301989883, 620756987, 1275068411, 2617245691, 5368709115, 11005853691, 22548578299, 46170898427

Offset

0,2

Comments

n-th difference of a(n), a(n-1), ..., a(0) is (7, 8, 9, ...).

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

G.f.: (-9*x^2 + 3*x + 1)/((1-x)*(1-2*x)^2).

a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). - Harvey P. Dale, Jul 07 2011

a(n) = 2^(n-1)*(n+12) - 5. - Vincenzo Librandi, Sep 28 2011

E.g.f.: exp(x)*(exp(x)*(6 + x) - 5). - Elmo R. Oliveira, Oct 29 2025

Mathematica

LinearRecurrence[{5, -8, 4}, {1, 8, 23}, 30] (* Harvey P. Dale, Jul 07 2011 *)
(* Alternative: *)
CoefficientList[ Series[ (-9x^2+3x+1)/((1-x)(1-2x)^2), {x, 0, 30}], x] (* Harvey P. Dale, Jul 07 2011 *)

Prog

(Magma) [2^(n-1)*(n+12)-5: n in [0..30]]; // Vincenzo Librandi, Sep 28 2011
(PARI) Vec((-9*x^2+3*x+1)/((1-x)*(1-2*x)^2) + O(x^40)) \\ Andrew Howroyd, Feb 15 2018

Crossrefs

Cf. A047858.

Sequence in context: A027054 A372674 A358246 * A002765 A048770 A055273

Adjacent sequences: A048464 A048465 A048466 * A048468 A048469 A048470

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved