A007752 Odd bisection of A007750.

1, 24, 391, 6240, 99457, 1585080, 25261831, 402604224, 6416405761, 102259887960, 1629741801607, 25973608937760, 413948001202561, 6597194410303224, 105141162563649031, 1675661406608081280

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

Cf. A007750, A007751.

Sequence in context: A020573 A022448 A025947 * A145602 A020447 A021894

Adjacent sequences: A007749 A007750 A007751 * A007753 A007754 A007755

Keyword

nonn

Author

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

Extensions

Edited by Michael Somos, Jul 27 2002

Status

approved