A107733 Column 2 of the array in A107735.

1, 3, 13, 11, 141, 43, 1485, 171, 15565, 683, 163021, 2731, 1707213, 10923, 17878221, 43691, 187223245, 174763, 1960627405, 699051, 20531956941, 2796203, 215013444813, 11184811, 2251650026701, 44739243, 23579585203405, 178956971, 246928622013645, 715827883, 2585870100909261, 2863311531

Offset: 3

Author

N. J. A. Sloane, Jun 10 2005

Keywords

• nonn

Comments

The second bisection [3, 11, 43, 171, 683, ...] is A007583. - Jean-François Alcover, Oct 22 2019 [noticed by Paul Curtz in a private e-mail].

References

• S. Mukai, An Introduction to Invariants and Moduli, Cambridge, 2003; see p. 483.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,17,0,-80,0,128,0,-64).

Crossrefs

Cf. A007583, A107735.

Programs

Mathematica

LinearRecurrence[{0, 17, 0, -80, 0, 128, 0, -64}, {1, 3, 13, 11, 141, 43, 1485, 171}, 32] (* Jean-François Alcover, Oct 22 2019 *)

Formula

a(n) = 1 + Sum_{j=1..g} 2^(2j-1) if n = 2g+2, = 1 + 4 Sum_{j=1..g} C(2g+1, 2j) 5^(j-1) if n = 2g+1.

From Chai Wah Wu, Jun 19 2016: (Start)

a(n) = 17*a(n-2) - 80*a(n-4) + 128*a(n-6) - 64*a(n-8) for n > 10.

G.f.: x^3*(-64*x^7 + 96*x^5 - 40*x^3 - 4*x^2 + 3*x + 1)/(64*x^8 - 128*x^6 + 80*x^4 - 17*x^2 + 1). (End)

Extensions

More terms from Emeric Deutsch, Jun 22 2005