A016201 Expansion of g.f. 1/((1-x)*(1-2*x)*(1-7*x)).

1, 10, 77, 554, 3909, 27426, 192109, 1345018, 9415637, 65910482, 461375421, 3229632042, 22607432485, 158252043778, 1107764339213, 7754350440026, 54280453211253, 379963172740914, 2659742209710685, 18618195469023370, 130327368285260741, 912291578001019490, 6386041046015525037

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-23,14).

Crossrefs

Cf. A016130, A023000.

Programs

Maple

a:=n->sum((7^(n-j+1)-2^(n-j+1))/5, j=0..n+1): seq(a(n), n=0..19); # Zerinvary Lajos, Jan 15 2007

Mathematica

CoefficientList[Series[1/((1-x)(1-2x)(1-7x)),{x,0,20}],x](* or *) LinearRecurrence[{10,-23,14},{1,10,77},20] (* Harvey P. Dale, Mar 06 2019 *)

Formula

a(n) = (49*7^n - 24*2^n + 5)/30. - Bruno Berselli, Feb 09 2011

a(0)=1, a(n) = 7*a(n-1) + 2^(n+1) - 1. - Vincenzo Librandi, Feb 09 2011

From Elmo R. Oliveira, Mar 27 2025: (Start)

E.g.f.: exp(x)*(49*exp(6*x) - 24*exp(x) + 5)/30.

a(n) = 10*a(n-1) - 23*a(n-2) + 14*a(n-3).

a(n) = A016130(n+1) - A023000(n+2). (End)

Extensions

More terms from Elmo R. Oliveira, Mar 27 2025