A139698 Binomial transform of [1, 25, 25, 25, ...].

1, 26, 76, 176, 376, 776, 1576, 3176, 6376, 12776, 25576, 51176, 102376, 204776, 409576, 819176, 1638376, 3276776, 6553576, 13107176, 26214376, 52428776, 104857576, 209715176, 419430376, 838860776, 1677721576, 3355443176, 6710886376, 13421772776, 26843545576

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) = 76 = (1, 2, 1) dot (1, 25, 25) = (1 + 50 + 25).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A139634, A139635, A139697.

Programs

Magma

[25*2^(n-1)-24 : n in [1..40]]; // Wesley Ivan Hurt, Jan 17 2017

Maple

seq(25*2^(n-1)-24,n=1..25); # Emeric Deutsch, May 03 2008

Mathematica

LinearRecurrence[{3,-2},{1,26},40] (* Harvey P. Dale, Jul 25 2021 *)

PARI

Vec(x*(23*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 11 2014

Formula

A007318 * [1, 25, 25, 25, ...].

a(n) = 25*2^(n-1)-24. - Emeric Deutsch, May 03 2008

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

a(n) = 3*a(n-1)-2*a(n-2). G.f.: x*(23*x+1) / ((x-1)*(2*x-1)). - Colin Barker, Mar 11 2014

Extensions

More terms from Emeric Deutsch, May 03 2008

More terms from Colin Barker, Mar 11 2014