A007751 Even bisection of A007750.

0, 7, 120, 1921, 30624, 488071, 7778520, 123968257, 1975713600, 31487449351, 501823476024, 7997688167041, 127461187196640, 2031381306979207, 32374639724470680, 515962854284551681, 8223031028828356224

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) = -4/7 + (2/7)*( (8-3*sqrt(7))^n + (8+3*sqrt(7))^n + (sqrt(7)/14)*( (8+3*sqrt(7))^n - (8-3*sqrt(7))^n ), with n>=0 - Paolo P. Lava, Jun 19 2008

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

Cf. A007750, A007752, A077412.

Sequence in context: A092612 A263943 A302718 * A193785 A253276 A156955

Adjacent sequences: A007748 A007749 A007750 * A007752 A007753 A007754

Keyword

nonn

Author

John C. Hallyburton, Jr. (hallyb(AT)vmsdev.enet.dec.com)

Extensions

Edited by Michael Somos, Jul 27 2002

Status

approved