A048512 a(n) = T(7,n), array T given by A048505.

1, 65, 210, 536, 1264, 2880, 6448, 14288, 31440, 68816, 149968, 325584, 704464, 1519568, 3268560, 7012304, 15007696, 32047056, 68288464, 145227728, 308281296, 653262800, 1382023120, 2919235536, 6157238224, 12968787920, 27279753168, 57310969808, 120259084240

Offset

0,2

Comments

n-th difference of a(n), a(n-1), ..., a(0) is (64, 81, 100, 121, ...).

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^2+29*n+196)*2^(n-2) - 48. - 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.: (216*x^3-227*x^2+58*x+1)/((x-1)*(2*x-1)^3). (End)

E.g.f.: exp(x)*(exp(x)*(49 + 15*x + x^2) - 48). - Elmo R. Oliveira, Oct 30 2025

Prog

(Magma) [(n^2+29*n+196) * 2^(n-2) - 48: n in [0..30]]; // Vincenzo Librandi, Sep 26 2011
(PARI) Vec((216*x^3-227*x^2+58*x+1)/((x-1)*(2*x-1)^3) + O(x^100)) \\ Colin Barker, Feb 25 2015

Crossrefs

Cf. A048505.

Sequence in context: A200867 A175795 A056777 * A237039 A305157 A038637

Adjacent sequences: A048509 A048510 A048511 * A048513 A048514 A048515

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

a(26) onward corrected by Sean A. Irvine, Nov 02 2025

Status

approved