A048469 a(n) = T(8,n), array T given by A047858.

1, 10, 29, 69, 153, 329, 697, 1465, 3065, 6393, 13305, 27641, 57337, 118777, 245753, 507897, 1048569, 2162681, 4456441, 9175033, 18874361, 38797305, 79691769, 163577849, 335544313, 687865849, 1409286137, 2885681145, 5905580025, 12079595513, 24696061945

Offset

0,2

Comments

n-th difference of a(n), a(n-1), ..., a(0) is (9, 10, 11, ...).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..3000

Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Formula

Main diagonal of the array defined by T(0,j) = j+1 for j>=0, T(i,0) = i+1 for i>=0, T(i,j) = T(i-1,j-1) + T(i-1,j) + 7. - Benoit Cloitre, Jun 17 2003

From Vincenzo Librandi, Sep 28 2011: (Start)

a(n) = 2^(n-1)*(n+16) - 7.

a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3), a(0)=1, a(1)=10, a(2)=29. (End)

G.f.: (1+5*x-13*x^2)/((1-x)*(1-2*x)^2). - Colin Barker, Feb 18 2016

E.g.f.: exp(x)*(exp(x)*(8 + x) - 7). - Elmo R. Oliveira, Oct 27 2025

Mathematica

LinearRecurrence[{5, -8, 4}, {1, 10, 29}, 40] (* Harvey P. Dale, Aug 15 2020 *)

Prog

(Magma) [2^(n-1)*(n+16)-7: n in [0..30]]; // Vincenzo Librandi, Sep 28 2011

Crossrefs

Cf. A047858.

Sequence in context: A068197 A079273 A271991 * A367343 A031129 A048772

Adjacent sequences: A048466 A048467 A048468 * A048470 A048471 A048472

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved