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A098300
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Member r=15 of the family of Chebyshev sequences S_r(n) defined in A092184.
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0
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0, 1, 15, 196, 2535, 32761, 423360, 5470921, 70698615, 913611076, 11806245375, 152567578801, 1971572279040, 25477872048721, 329240764354335, 4254652064557636, 54981236074894935, 710501416909076521
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| a(n)= 2*(T(n, 13/2)-1)/11 with twice the Chebyshev's polynomials of the first kind evaluated at x=13/2: 2*T(n, 13/2)=A078363(n)=((13+sqrt(165))^n + (13-sqrt(165))^n)/2^n.
a(n)= 13*a(n-1) - a(n-2) + 2, n>=2, a(0)=0, a(1)=1.
a(n)= 14*a(n-1) - 14*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=15.
G.f.: x*(1+x)/((1-x)*(1-13*x+x^2)) = x*(1+x)/(1-14*x+14*x^2-x^3) (from the Stephan link, see A092184).
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CROSSREFS
| Sequence in context: A172204 A015673 A125472 * A185899 A152587 A060337
Adjacent sequences: A098297 A098298 A098299 * A098301 A098302 A098303
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004
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