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

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..3000
• Index entries for linear recurrences with constant coefficients, signature (5, -8, 4).

Crossrefs

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

Programs

Magma

[2^(n-1)*(n+12)-5: n in [0..30]]; // Vincenzo Librandi, Sep 28 2011

Mathematica

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

PARI

Vec((-9*x^2+3*x+1)/((1-x)*(1-2*x)^2) + O(x^40)) \\ Andrew Howroyd, Feb 15 2018

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