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A030240
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Scaled Chebyshev U-polynomials evaluated at sqrt(7)/2.
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9
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1, 7, 42, 245, 1421, 8232, 47677, 276115, 1599066, 9260657, 53631137, 310593360, 1798735561, 10416995407, 60327818922, 349375764605, 2023335619781, 11717718986232, 67860683565157, 393000752052475
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A030221. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2009]
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REFERENCES
| A. F. Horadam, Special properties of the sequence W_n(a,b; p,q), Fib. Quart., 5.5 (1967), 424-434. Case n->n+1, a=0,b=1; p=7, q=-7.
W. Lang, On polynomials related to powers of the generating function of Catalan's numbers, Fib. Quart. 38,5 (2000) 408-419; Eqs. (38) and (45), lhs, m=7.
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LINKS
| Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| a(n) = 7*a(n-1)-7*a(n-2), a(-1)=0, a(0)=1; a(n)=sqrt(7)^n*U(n, sqrt(7)/2); g.f.:1/(1-7*x+7*x^2); a(2*k)=7^k*A030221(k); a(2*k-1)=7^k*A004254(k)
a(n)=Sum_{k, 0<=k<=n} A109466(n,k)*7^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 28 2008]
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MATHEMATICA
| Join[{a=1, b=7}, Table[c=7*b-7*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 18 2011*)
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PROG
| (Other) sage: [lucas_number1(n, 7, 7) for n in xrange(1, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
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CROSSREFS
| Sequence in context: A164072 A111995 A050152 * A054890 A102594 A053142
Adjacent sequences: A030237 A030238 A030239 * A030241 A030242 A030243
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KEYWORD
| nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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