A047851 a(n) = T(3,n), array T given by A047848.

1, 2, 8, 44, 260, 1556, 9332, 55988, 335924, 2015540, 12093236, 72559412, 435356468, 2612138804, 15672832820, 94036996916, 564221981492, 3385331888948, 20311991333684, 121871948002100, 731231688012596, 4387390128075572, 26324340768453428, 157946044610720564, 947676267664323380

Offset

0,2

Comments

n-th difference of a(n), a(n-1), ..., a(0) is 5^(n-1) for n=1, 2, 3, ...

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (7,-6).

Formula

a(n) = (6^n + 4)/5. - Ralf Stephan, Feb 14 2004

From Philippe Deléham, Oct 05 2009: (Start)

a(0) = 1, a(1) = 2, a(n) = 7*a(n-1) - 6*a(n-2) for n > 1.

G.f.: (1 - 5*x)/(1 - 7*x + 6*x^2). (End)

a(n) = 6*a(n-1) - 4 (with a(0)=1). - Vincenzo Librandi, Aug 06 2010

exp(x)*(exp(5*x) + 4)/5. - Elmo R. Oliveira, Aug 29 2024

Maple

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=6*a[n-1]+1 od: seq(a[n]+1, n=0..20); # Zerinvary Lajos, Mar 20 2008

Crossrefs

Cf. A047848.

Sequence in context: A362413 A362408 A291697 * A177260 A121747 A261266

Adjacent sequences: A047848 A047849 A047850 * A047852 A047853 A047854

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

a(21)-a(24) from Elmo R. Oliveira, Aug 29 2024

Status

approved