A047861 a(n) = T(4,n), array T given by A047858.

1, 6, 17, 41, 93, 205, 445, 957, 2045, 4349, 9213, 19453, 40957, 86013, 180221, 376829, 786429, 1638397, 3407869, 7077885, 14680061, 30408701, 62914557, 130023421, 268435453, 553648125, 1140850685, 2348810237, 4831838205, 9932111869, 20401094653, 41875931133

Offset

0,2

Comments

n-th difference of a(n), a(n-1), ..., a(0) is (5, 6, 7, ...).

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

From Benoit Cloitre, Jun 17 2003: (Start)

Main diagonal of the array defined by T(0,j) = j+1 j>=0, T(i,0) = i+1 i>=0, T(i,j) = T(i-1,j-1) + T(i-1,j) + 3.

a(n) = 2^(n-1)*(n+8) - 3. (End)

a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3), a(0)=1, a(1)=6, a(2)=17. - Vincenzo Librandi, Sep 28 2011

G.f.: (1+x-5*x^2)/((1-x)*(1-2*x)^2). - Colin Barker, Feb 17 2016

E.g.f.: exp(x)*(exp(x)*(4+x) - 3). - Elmo R. Oliveira, Oct 26 2025

Prog

(Magma) [2^(n-1)*(n+8)-3: n in [0..30]]; // Vincenzo Librandi, Sep 28 2011
(PARI) Vec((1+x-5*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ Colin Barker, Feb 17 2016

Crossrefs

Cf. A047858.

Sequence in context: A220407 A387334 A013319 * A370589 A343518 A365409

Adjacent sequences: A047858 A047859 A047860 * A047862 A047863 A047864

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved