A048490 a(n) = T(7,n), array T given by A048483.

1, 9, 25, 57, 121, 249, 505, 1017, 2041, 4089, 8185, 16377, 32761, 65529, 131065, 262137, 524281, 1048569, 2097145, 4194297, 8388601, 16777209, 33554425, 67108857, 134217721, 268435449, 536870905, 1073741817, 2147483641, 4294967289, 8589934585

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

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

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Programs

Mathematica

a=1; lst={a}; k=8; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 16 2008 *)

PARI

Vec((6*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Nov 26 2014

Formula

a(n) = 8 * 2^n - 7. - Ralf Stephan, Jan 09 2009

Equals binomial transform of [1, 8, 8, 8, ...]. - Gary W. Adamson, Apr 29 2008

a(n) = 2*a(n-1) + 7 for n > 0, a(0)=1. - Vincenzo Librandi, Aug 06 2010

For n>=1, a(n) = 6<+>(n+3), where the operation <+> is defined in A206853. - Vladimir Shevelev, Feb 17 2012

From Colin Barker, Nov 26 2014: (Start)

a(n) = 3*a(n-1) - 2*a(n-2).

G.f.: (6*x+1) / ((x-1)*(2*x-1)). (End)

Extensions

More terms from Colin Barker, Nov 26 2014