A139700 Binomial transform of [1, 30, 30, 30, ...].

1, 31, 91, 211, 451, 931, 1891, 3811, 7651, 15331, 30691, 61411, 122851, 245731, 491491, 983011, 1966051, 3932131, 7864291, 15728611, 31457251, 62914531, 125829091, 251658211, 503316451, 1006632931, 2013265891, 4026531811, 8053063651, 16106127331

Offset: 1

Author

Gary W. Adamson, Apr 29 2008

Keywords

• nonn
• easy

Comments

The binomial transform of [1, c, c, c, ...] has the terms a(n) = 1 - c + c*2^(n-1) if the offset 1 is chosen. The o.g.f. of the a(n) is x{1+(c-2)x}/{(2x-1)(x-1)}. This applies to A139634 with c=10, to A139635 with c=11, to A139697 with c=12, to A139698 with c=25 and to A099003, A139700, A139701 accordingly. - R. J. Mathar, May 11 2008

Examples

			a(3) = 91 = (1, 2, 1) dot (1, 30, 30) = (1 + 60 + 30).
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A139699, A139698, A139697, A139635, A139634.

Programs

Maple

seq(30*2^(n-1)-29,n=1..27); # Emeric Deutsch, May 07 2008

Mathematica

LinearRecurrence[{3,-2},{1,31},30] (* Harvey P. Dale, Apr 18 2018 *)

PARI

Vec(x*(28*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 11 2014

Formula

A007318 * [1, 30, 30, 30, ...].

a(n) = 30*2^(n-1) - 29. - Emeric Deutsch, May 07 2008

a(n) = 2*a(n-1) + 29 (with a(1)=1). - Vincenzo Librandi, Nov 24 2010

From Colin Barker, Mar 11 2014: (Start)

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

G.f.: x*(28*x+1) / ((x-1)*(2*x-1)). (End)

Extensions

More terms from Emeric Deutsch, May 07 2008

More terms from Colin Barker, Mar 11 2014