A107732 Column 1 of the array in A107735.

1, 2, 5, 4, 21, 8, 85, 16, 341, 32, 1365, 64, 5461, 128, 21845, 256, 87381, 512, 349525, 1024, 1398101, 2048, 5592405, 4096, 22369621, 8192, 89478485, 16384, 357913941, 32768, 1431655765, 65536, 5726623061, 131072, 22906492245, 262144, 91625968981, 524288, 366503875925

Offset

3,2

References

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

Links

Chai Wah Wu, Table of n, a(n) for n = 3..3324

Index entries for linear recurrences with constant coefficients, signature (0,7,0,-14,0,8).

Formula

a(2*k+2) = 2^k = A000079(k), a(2*k+1) = (4^k-1)/3 = A002450(k) = A001045(2*k).

a(n) = 7*a(n-2) - 14*a(n-4) + 8*a(n-6) for n > 8. - Chai Wah Wu, Jun 19 2016

G.f.: x^3*(1 + 2*x - 2*x^2 - 10*x^3 + 8*x^5)/(1 - 7*x^2 + 14*x^4 - 8*x^6). - Chai Wah Wu, Jun 19 2016

a(n) = (3*(1 + (-1)^n)*2^(n/2) - (1 - (-1)^n)*(2 - 2^n))/12. - Colin Barker, Mar 26 2019

a(n) = (2^n - 2)/6 if n is odd else 2^(n/2 - 1). - Peter Luschny, Mar 26 2019

Mathematica

Table[(3 (1 + (-1)^n) 2^(n/2) - (1 - (-1)^n) (2 - 2^n))/12, {n, 3, 50}] (* Bruno Berselli, Mar 26 2019 *)

Prog

(PARI) Vec(x^3*(1 + 2*x - 2*x^2 - 10*x^3 + 8*x^5) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + 2*x)*(1 - 2*x^2)) + O(x^40)) \\ Colin Barker, Mar 26 2019
(Sage)
def a(n): return (2^n-2)//6 if is_odd(n) else 2^(n//2-1))
print([a(n) for n in (3..41)]) # Peter Luschny, Mar 26 2019

Crossrefs

Cf. A000079, A001045, A002450, A107735.

Sequence in context: A255544 A019152 A013621 * A349475 A111364 A128202

Adjacent sequences: A107729 A107730 A107731 * A107733 A107734 A107735

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 10 2005

Extensions

More terms from Chai Wah Wu, Jun 19 2016

Status

approved