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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
(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.
Index to sequences with linear recurrences with constant coefficients, signature (7,-7,1).
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FORMULA
| 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)).
Partial sums of A001109 - Barry Williams May 03 2000.
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]
Using b()=A001109(), a(2n) = b(n)*(b(n) + b(n-1)) and a(2n-1) = b(n)*(b(n) + b(n+1)) [From Kenneth J Ramsey (ramsey2879(AT)msn.com), Sep 10 2010]
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=6*b-a+1; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 18 2011*)
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CROSSREFS
| Cf. A001653, A053141.
Cf. A001652, A046090.
Sequence in context: A030240 A054890 A102594 * A162941 A094168 A163345
Adjacent sequences: A053139 A053140 A053141 * A053143 A053144 A053145
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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