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A145934 Expansion of 1/(1-x*(1-6*x)). 10
1, 1, -5, -11, 19, 85, -29, -539, -365, 2869, 5059, -12155, -42509, 30421, 285475, 102949, -1609901, -2227595, 7431811, 20797381, -23793485, -148577771, -5816861, 885649765, 920550931, -4393347659, -9916653245, 16443432709 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums of Riordan array (1, x(1-6x)).

For positive n, a(n) equals the determinant of the n X n tridiagonal matrix with 1's along the main diagonal, 3's along the superdiagonal, and 2's along the subdiagonal (see Mathematica code below). - John M. Campbell, Jul 08 2011

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..2569

Index entries for linear recurrences with constant coefficients, signature (1,-6).

FORMULA

a(n) = Sum_{k=0..n} A109466(n,k)*6^(n-k).

a(n) = a(n-1) - 6*a(n-2); a(0)=1, a(1)=1. - Philippe Deléham, Oct 25 2008

a(n) = (1/46)*i*(1/2 - (1/2)*i*sqrt(23))^n*sqrt(23) + (1/2)*(1/2 - (1/2)*i*sqrt(23))^n - (1/46)*i*(1/2 + (1/2)*i*sqrt(23))^n*sqrt(23) + (1/2)*(1/2 + (1/2)*i*sqrt(23))^n, with n >= 0 and i=sqrt(-1). - Paolo P. Lava, Nov 18 2008

MATHEMATICA

Join[{a=1, b=1}, Table[c=b-6*a; a=b; b=c, {n, 80}]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2011*)

Table[Det[Array[KroneckerDelta[#1, #2] + KroneckerDelta[#1, #2 + 1]*2 + KroneckerDelta[#1, #2 - 1]*3 &, {n, n}]], {n, 1, 40}] (* John M. Campbell, Jul 08 2011 *)

LinearRecurrence[{1, -6}, {1, 1}, 30] (* G. C. Greubel, Jan 14 2018 *)

PROG

(Sage) [lucas_number1(n, 1, 6) for n in xrange(1, 29)] # Zerinvary Lajos, Apr 22 2009

(PARI) Vec(1/(1-x*(1-6*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012

(MAGMA) I:=[1, 1]; [n le 2 select I[n] else Self(n-1) - 6*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 14 2018

CROSSREFS

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

Sequence in context: A267603 A297365 A128927 * A033913 A088124 A029456

Adjacent sequences:  A145931 A145932 A145933 * A145935 A145936 A145937

KEYWORD

sign,easy

AUTHOR

Philippe Deléham, Oct 25 2008

STATUS

approved

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Last modified February 22 12:00 EST 2018. Contains 299452 sequences. (Running on oeis4.)