A145976 Expansion of 1/(1-x*(1-7*x)).

1, 1, -6, -13, 29, 120, -83, -923, -342, 6119, 8513, -34320, -93911, 146329, 803706, -220597, -5846539, -4302360, 36623413, 66739933, -189623958, -656803489, 670564217, 5268188640, 574239121, -36303081359, -40322755206, 213798814307

Offset: 0

Author

Philippe Deléham, Oct 26 2008

Keywords

• sign
• easy

Comments

Row sums of Riordan array (1,x(1-7x)).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1500
• Taras Goy and Mark Shattuck, Determinants of Toeplitz-Hessenberg Matrices with Generalized Leonardo Number Entries, Ann. Math. Silesianae (2023). See p. 17.
• Index entries for linear recurrences with constant coefficients, signature (1,-7).

Crossrefs

Cf. A010892, A107920, A106852, A106853, A106854, A145934.

Programs

Magma

I:=[1,1]; [n le 2 select I[n] else Self(n-1) - 7*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 19 2018

Mathematica

Join[{a=1,b=1},Table[c=b-7*a;a=b;b=c,{n,80}]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2011 *)
CoefficientList[Series[1/(1-x(1-7x)),{x,0,50}],x] (* or *) LinearRecurrence[{1,-7},{1,1},50] (* Harvey P. Dale, May 11 2011 *)

PARI

Vec(1/(1-x*(1-7*x)) + O(x^40)) \\ Michel Marcus, Jan 29 2016

Sage

[lucas_number1(n,1,7) for n in range(1, 29)] # Zerinvary Lajos, Apr 22 2009

Formula

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

a(n) = Sum_{k=0..n} A109466(n,k)*7^(n-k).

Extensions

Corrected by Zerinvary Lajos, Apr 22 2009

Corrected by D. S. McNeil, Aug 20 2010