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A145976 Expansion of 1/(1-x*(1-7*x)). 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1500

Index entries for linear recurrences with constant coefficients, signature (1, -7).

FORMULA

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

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

a(n) = -(1/18)*I*sqrt(3)*[(1/2)+(3/2)*I*sqrt(3)]^n+(1/18)*I*sqrt(3)*[(1/2)-(3/2)*I *sqrt(3)]^n+(1/2)*[(1/2)-(3/2)*I*sqrt(3)]^n+(1/2)*[(1/2)+(3/2)*I*sqrt(3)]^n, with n>=0 and I=sqrt(-1). [Paolo P. Lava, Nov 18 2008]

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 *)

PROG

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

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

CROSSREFS

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

Sequence in context: A016071 A086652 A159694 * A101622 A256871 A192304

Adjacent sequences:  A145973 A145974 A145975 * A145977 A145978 A145979

KEYWORD

sign

AUTHOR

Philippe Deléham, Oct 26 2008

EXTENSIONS

Corrected by Zerinvary Lajos, Apr 22 2009

Corrected by D. S. McNeil, Aug 20 2010

STATUS

approved

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Last modified September 26 04:27 EDT 2017. Contains 292502 sequences.