A016198 Expansion of g.f. 1/((1-x)*(1-2*x)*(1-5*x)).

1, 8, 47, 250, 1281, 6468, 32467, 162590, 813461, 4068328, 20343687, 101722530, 508620841, 2543120588, 12715635707, 63578244070, 317891351421, 1589457019248, 7947285620527, 39736429151210, 198682147853201, 993410743460308, 4967053725690147, 24835268645227950

Offset: 0

Author

N. J. A. Sloane, Dec 11 1999

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-17,10).

Crossrefs

Cf. A000225, A000392, A002275, A002452, A003462, A003463, A003464, A016123, A016125, A016208, A016209, A016218, A016256, A023000, A023001.

Cf. A016127.

Programs

Maple

a:=n->sum((5^(n-j)-2^(n-j))/3,j=0..n): seq(a(n), n=1..20); # Zerinvary Lajos, Jan 04 2007

Mathematica

Join[{a=1,b=8},Table[c=7*b-10*a+1;a=b;b=c,{n,60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 06 2011 *)

Formula

a(n) = (25*5^n - 16*2^n + 3)/12. - Bruno Berselli, Feb 09 2011

a(n) = [(5^0-2^0) + (5^1-2^1) + ... + (5^n-2^n)]/3. - r22lou(AT)cox.net, Nov 14 2005

a(0)=1, a(n) = 5*a(n-1) + 2^(n+1) - 1. - Vincenzo Librandi, Feb 07 2011

From Elmo R. Oliveira, Mar 26 2025: (Start)

E.g.f.: exp(x)*(25*exp(4*x) - 16*exp(x) + 3)/12.

a(n) = 8*a(n-1) - 17*a(n-2) + 10*a(n-3).

a(n) = A016127(n+1) - A003463(n+2). (End)

Extensions

More terms from Wesley Ivan Hurt, May 05 2014