A048508 a(n) = T(3,n), array T given by A048505.

1, 17, 58, 160, 408, 1000, 2392, 5624, 13048, 29944, 68088, 153592, 344056, 765944, 1695736, 3735544, 8191992, 17891320, 38928376, 84410360, 182452216, 393215992, 845152248, 1811939320, 3875536888, 8271167480, 17616076792, 37446746104, 79456894968, 168309030904

Offset

0,2

Comments

n-th difference of a(n), a(n-1), ..., a(0) is (16, 25, 36, 49, 64, ...).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (7,-18,20,-8).

Formula

a(n) = (n+4)*(n+9) * 2^(n-2) - 8. - Ralf Stephan, Feb 05 2004

From Colin Barker, Feb 25 2015: (Start)

a(n) = 7*a(n-1) - 18*a(n-2) + 20*a(n-3) - 8*a(n-4).

G.f.: (40*x^3-43*x^2+10*x+1)/((x-1)*(2*x-1)^3). (End)

E.g.f.: exp(x)*(exp(x)*(9 + 7*x + x^2) - 8). - Elmo R. Oliveira, Oct 28 2025

Prog

(Magma) [(n+4)*(n+9) * 2^(n-2) - 8: n in [0..30]]; // Vincenzo Librandi, Sep 26 2011
(PARI) Vec((40*x^3-43*x^2+10*x+1)/((x-1)*(2*x-1)^3) + O(x^100)) \\ Colin Barker, Feb 25 2015

Crossrefs

Cf. A048505.

Sequence in context: A146453 A146046 A396290 * A020879 A029914 A058319

Adjacent sequences: A048505 A048506 A048507 * A048509 A048510 A048511

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved