OFFSET
1,2
REFERENCES
Mentioned in a problem on p. 334 of Two-Year College Math. Jnl., Vol. 25, 1994.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..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*(1+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) -53*ChebyshevU(n-1, 8) -4)/7. - G. C. Greubel, Mar 04 2020
E.g.f.: (exp(8*x)*(4*cosh(3*sqrt(7)*x) - sqrt(7)*sinh(3*sqrt(7)*x)) - 4*exp(x))/7. - Stefano Spezia, Mar 14 2020
MAPLE
seq( simplify( (4*ChebyshevU(n, 8) - 53*ChebyshevU(n-1, 8) -4)/7), n=1..20); # G. C. Greubel, Mar 04 2020
MATHEMATICA
Table[(4*ChebyshevU[n, 8] -53*ChebyshevU[n-1, 8] -4)/7, {n, 20}] (* G. C. Greubel, Mar 04 2020 *)
PROG
(PARI) a(n)=local(w); w=8+3*quadgen(28); imag(1/w^n)+4*(real(1/w^n)-1)/7
(PARI) vector(30, n, (4*polchebyshev(n, 2, 8) -53*polchebyshev(n-1, 2, 8) -4)/7 ) \\ G. C. Greubel, Mar 04 2020
(Magma) I:=[1, 24, 391]; [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, Mar 04 2020
(Sage) [(4*chebyshev_U(n, 8) -53*chebyshev_U(n-1, 8) -4)/7 for n in (1..30)] # G. C. Greubel, Mar 04 2020
(GAP) a:=[1, 24, 391];; for n in [4..30] do a[n]:=17*a[n-1]-17*a[n-2]+a[n-3]; od; a; # G. C. Greubel, Mar 04 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
John C. Hallyburton, Jr. (hallyb(AT)vmsdev.enet.dec.com)
EXTENSIONS
Edited by Michael Somos, Jul 27 2002
STATUS
approved