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

3,2

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

Table of n, a(n) for n=3..34.

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

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)

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 *)

Crossrefs

Cf. A007583, A107735.

Sequence in context: A360967 A214811 A121565 * A273076 A272825 A054767

Adjacent sequences: A107730 A107731 A107732 * A107734 A107735 A107736

Keyword

nonn

Author

N. J. A. Sloane, Jun 10 2005

Extensions

More terms from Emeric Deutsch, Jun 22 2005

Status

approved