A048480 a(n) = T(8,n), array T given by A048472.

1, 10, 37, 109, 289, 721, 1729, 4033, 9217, 20737, 46081, 101377, 221185, 479233, 1032193, 2211841, 4718593, 10027009, 21233665, 44826625, 94371841, 198180865, 415236097, 868220929, 1811939329, 3774873601, 7851737089, 16307453953, 33822867457, 70061654017

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy
• changed

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Crossrefs

Cf. A008591 (contains n-th difference of a(n),a(n-1),...,a(0)).

Cf. A048472.

Programs

Magma

[9*n * 2^(n-1) + 1: n in [0..30]]; // Vincenzo Librandi, Sep 23 2011

Mathematica

Table[9*n*2^(n-1)+1,{n,0,30}] (* or *) LinearRecurrence[{5,-8,4},{1,10,37},30] (* Harvey P. Dale, Jul 09 2014 *)

PARI

Vec((1+5*x-5*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ Colin Barker, Feb 18 2016

Formula

a(n) = 9*n * 2^(n-1) + 1.

a(0)=1, a(1)=10, a(2)=37, a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3). - Harvey P. Dale, Jul 09 2014

G.f.: (1+5*x-5*x^2) / ((1-x)*(1-2*x)^2). - Colin Barker, Feb 18 2016

E.g.f.: exp(x)*(1 + 9*exp(x)*x). - Stefano Spezia, Aug 28 2025