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Search: id:A053142
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| 0, 1, 7, 42, 246, 1435, 8365, 48756, 284172, 1656277, 9653491, 56264670, 327934530, 1911342511, 11140120537, 64929380712, 378436163736, 2205687601705, 12855689446495, 74928449077266, 436715005017102
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OFFSET
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0,3
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LINKS
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Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n)= (A001653(n)-1)/4.
a(n) := 6*a(n-1)-a(n-2)+1, a(0)=0, a(1)=1; G.f.: x/((1-x)*(1-6*x+x^2)).
a(n+1)=sum{k=0..n, S(k, 6)}=sum{k=0..n, U(n, 3)} Chebyshev polynomials of 2nd kind, A049310; a(n+1)=(sqrt(2)-1)^(2n)(5/8-7sqrt(2)/16)+(sqrt(2)+1)^(2n)(7sqrt(2)/16 + 5/8)-1/4 - Paul Barry (pbarry(AT)wit.ie), Nov 14 2003
a(n) = 7a(n-1)-7a(n-2)+a(n-3); a(n) = -(1/4)+(1-sqrt(2))/(-8*sqrt(2))*(3-2*sqrt(2))^n+(1+sqrt(2))/(8*sqrt(2))*(3+2*sqrt(2))^n. - Antonio Alberto Olivares (tonioolivares(AT)todito.com), Jan 13 2004
a(n)=sum{k=0..n, sum{j=0..2k, (-1)^(j+1)*Pell(j)*Pell(2k-j)}}, Pell(n)=A000129(n). [From Paul Barry (pbarry(AT)wit.ie), Oct 23 2009]
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CROSSREFS
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Cf. A001653, A053141.
Cf. A001653, A053141. Partial sums of A001109 - Barry Williams May 03 2000.
Cf. A001652, A046090, A001653.
Sequence in context: A030240 A054890 A102594 this_sequence A094168 A003949 A033133
Adjacent sequences: A053139 A053140 A053141 this_sequence A053143 A053144 A053145
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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