A047851 a(n) = A047848(3,n).

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

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

n-th difference of a(n), a(n-1), ..., a(0) is A000351(n-1) for n >= 1.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-6).

Crossrefs

Cf. A000351, A047848.

Programs

Magma

[(6^n + 4)/5: n in [0..40]]; // G. C. Greubel, Jan 11 2025

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

Mathematica

(6^Range[0,40] +4)/5 (* G. C. Greubel, Jan 11 2025 *)

Python

def A047851(n): return (pow(6,n) + 4)//5
print([A047851(n) for n in range(41)]) # G. C. Greubel, Jan 11 2025

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

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

Extensions

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