OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..825
K. R. S. Sastry, Problem 533 The College Mathematics Journal, 25, issue 4, 1994, p. 334.
K. R. S. Sastry, Square Products of Sums of Squares The College Mathematics Journal, 26, issue 4, 1995, p. 333.
Index entries for linear recurrences with constant coefficients, signature (17,-17,1).
FORMULA
G.f.: x*(7 + x)/((1-x)*(1-16*x+x^2)).
a(n) = 16*a(n-1) - a(n-2) + 8.
a(n) = (4*ChebyshevU(n,8) - 11*ChebyshevU(n-1,8) -4)/7. - G. C. Greubel, Feb 10 2020
E.g.f.: (cosh(x) + sinh(x))*(-4 + (cosh(7*x) + sinh(7*x))*(4*cosh(3*sqrt(7)*x) + sqrt(7)*sinh(3*sqrt(7)*x)))/7. - Stefano Spezia, Feb 20 2020
MAPLE
seq(simplify((4*ChebyshevU(n, 8) -11*ChebyshevU(n-1, 8) -4)/7)), n = 0..30); # G. C. Greubel, Feb 10 2020
MATHEMATICA
Table[(4*ChebyshevU[n, 8] -11*ChebyshevU[n-1, 8] -4)/7, {n, 0, 30}] (* G. C. Greubel, Feb 10 2020 *)
LinearRecurrence[{17, -17, 1}, {0, 7, 120}, 20] (* Harvey P. Dale, Dec 01 2022 *)
PROG
(PARI) a(n)=local(w); w=8+3*quadgen(28); imag(w^n)+4*(real(w^n)-1)/7
(PARI) vector(31, n, my(m=n-1); (4*polchebyshev(m, 2, 8) -11*polchebyshev(m-1, 2, 8) -4)/7 ) \\ G. C. Greubel, Feb 10 2020
(Magma) I:=[0, 7, 120]; [n le 3 select I[n] else 17*Self(n-1) -17*Self(n-2) +Self(n-3): n in [1..30]]; // G. C. Greubel, Feb 10 2020
(Sage) [(4*chebyshev_U(n, 8) -11*chebyshev_U(n-1, 8) -4)/7 for n in (0..30)] # G. C. Greubel, Feb 10 2020
(GAP) a:=[0, 7, 120];; for n in [4..30] do a[n]:=17*a[n-1]-17*a[n-2]+a[n-3]; od; a; # G. C. Greubel, Feb 10 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
John C. Hallyburton, Jr. (hallyb(AT)vmsdev.enet.dec.com)
EXTENSIONS
Edited by Michael Somos, Jul 27 2002
STATUS
approved