0,2

a(143+286k)-1 and a(143+286k)+1 are consecutive odd powerful numbers. See A076445. - T. D. Noe (noe(AT)sspectra.com), May 04 2006

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n+1)^2 - 143*b(n)^2 = 1, n>=0, with the companion sequence b(n)=A077423(n).

a(n)=24*a(n-1) - a(n-2), a(-1) := 12, a(0)=1.

a(n)= T(n, 12)= (S(n, 24)-S(n-2, 24))/2 = S(n, 24)-11*S(n-1, 24) with T(n, x), resp. S(n, x), Chebyshev's polynomials of the first, resp. second, kind. See A053120 and A049310. S(n, 24)=A077423(n).

a(n)= (ap^n + am^n)/2 with ap := 12+sqrt(143) and am := 12-sqrt(143).

a(n)= sum(((-1)^k)*(n/(2*(n-k)))*binomial(n-k, k)*(2*12)^(n-2*k), k=0..floor(n/2)), n>=1.

a(n+1)=sqrt(1 + 143*A077423(n)^2), n>=0.

G.f.: (1-12*x)/(1-24*x+x^2).

sage: [lucas_number2(n, 24, 1)/2 for n in xrange(0, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 26 2008

Cf. A090732.

Adjacent sequences: A077421 A077422 A077423 this_sequence A077425 A077426 A077427

Sequence in context: A115461 A009604 A079519 this_sequence A001164 A041267 A041264

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 2002