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

Author

N. J. A. Sloane, Jun 10 2005

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000079, A001045, A002450, A107735.

Programs

Mathematica

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

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

SageMath

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

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

Extensions

More terms from Chai Wah Wu, Jun 19 2016