A007751 Even bisection of A007750.

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

Offset: 0

Author

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

Keywords

• nonn

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).

Crossrefs

Cf. A007750, A007752, A077412.

Programs

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

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

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 *)

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

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

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

Extensions

Edited by Michael Somos, Jul 27 2002