A047852 a(n) = T(4,n), array T given by A047848.

1, 2, 9, 58, 401, 2802, 19609, 137258, 960801, 6725602, 47079209, 329554458, 2306881201, 16148168402, 113037178809, 791260251658, 5538821761601, 38771752331202, 271402266318409, 1899815864228858, 13298711049602001, 93090977347214002, 651636841430498009, 4561457890013486058

Offset

0,2

Comments

n-th difference of a(n), a(n-1), ..., a(0) is 6^(n-1) for n=1, 2, 3, ...

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (8,-7).

Formula

a(n) = (7^n + 5)/6. - Ralf Stephan, Feb 14 2004

From Philippe Deléham, Oct 06 2009: (Start)

a(0) = 1, a(1) = 2, a(n) = 8*a(n-1) - 7*a(n-2) for n > 1.

G.f.: (1 - 6*x)/(1 - 8*x + 7*x^2). (End)

a(n) = 7*a(n-1) - 5, with a(0)=1. - Vincenzo Librandi, Aug 06 2010

E.g.f.: exp(x)*(exp(6*x) + 5)/6. - Elmo R. Oliveira, Aug 29 2024

Maple

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=7*a[n-1]+1 od: seq(a[n]+1, n=0..19); # Zerinvary Lajos, Mar 20 2008

Crossrefs

Cf. A047848.

Sequence in context: A124405 A300343 A141787 * A240881 A224127 A366401

Adjacent sequences: A047849 A047850 A047851 * A047853 A047854 A047855

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

a(20)-a(23) from Elmo R. Oliveira, Aug 29 2024

Status

approved