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

1,2

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

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

Example

a(3) = 76 = (1, 2, 1) dot (1, 25, 25) = (1 + 50 + 25).

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 *)

Prog

(PARI) Vec(x*(23*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 11 2014
(Magma) [25*2^(n-1)-24 : n in [1..40]]; // Wesley Ivan Hurt, Jan 17 2017

Crossrefs

Cf. A139634, A139635, A139697.

Sequence in context: A251074 A304657 A262221 * A124719 A126380 A083578

Adjacent sequences: A139695 A139696 A139697 * A139699 A139700 A139701

Keyword

nonn,easy

Author

Gary W. Adamson, Apr 29 2008

Extensions

More terms from Emeric Deutsch, May 03 2008

More terms from Colin Barker, Mar 11 2014

Status

approved