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A049072
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Expansion of 1/(1-3*x+4*x^2).
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4
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1, 3, 5, 3, -11, -45, -91, -93, 85, 627, 1541, 2115, 181, -7917, -24475, -41757, -27371, 84915, 364229, 753027, 802165, -605613, -5025499, -12654045, -17860139, -2964237, 62547845, 199500483, 348310069, 246928275, -652455451, -2945079453, -6225416555
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Comment from Sharon Sela (sharonsela(AT)hotmail.com), Jan 22 2002: a(n) is the determinant of the following tri-diagonal n X n matrix:
[3 2 0 0 .... ]
[2 3 2 0 .... ]
[0 2 3 2 0 .. ]
[. 0 2 3 2 .. ]
[. . . . .... ]
[. . . 2 3 2 0]
[. . . 0 2 3 2]
[. . . 0 0 2 3]
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REFERENCES
| B. R. Myers, On spanning trees..., SIAM Rev., 17 (1975), 465-474.
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FORMULA
| G.f.: 1/(1-3*x+4*x^2).
a(n)=(-1)^n*sum{k=0..n, binomial(2n-k+1, k)(-2)^k} - Paul Barry (pbarry(AT)wit.ie), Jan 17 2005
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MATHEMATICA
| Join[{a=1, b=3}, Table[c=3*b-4*a; a=b; b=c, {n, 100}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 17 2011*)
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PROG
| (PARI) a(n)=if(n<0, 0, 2^n*subst(-3*poltchebi(n+1)+4*poltchebi(n), 'x, 3/4)*4/7) /* Michael Somos Sep 15 2005 */
(PARI) a(n)=if(n<0, 0, matdet(matrix(n, n, i, j, if(abs(i-j)<2, 3-abs(i-j))))) /* Michael Somos Sep 15 2005 *
(Other) sage: [lucas_number1(n, 3, 4) for n in xrange(1, 34)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
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CROSSREFS
| Cf. A025170.
Sequence in context: A105445 A178095 A177904 * A059887 A023585 A089948
Adjacent sequences: A049069 A049070 A049071 * A049073 A049074 A049075
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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