A390532 Sequences A001477 and A000079 interlaced.

0, 1, 1, 2, 2, 4, 3, 8, 4, 16, 5, 32, 6, 64, 7, 128, 8, 256, 9, 512, 10, 1024, 11, 2048, 12, 4096, 13, 8192, 14, 16384, 15, 32768, 16, 65536, 17, 131072, 18, 262144, 19, 524288, 20, 1048576, 21, 2097152, 22, 4194304, 23, 8388608, 24, 16777216, 25, 33554432, 26, 67108864, 27

Offset

0,4

References

Konrad Knopp, Theory and application of infinite series, Blackie & Son Limited, London and Glasgow, 1954. See p. 67.

Links

Table of n, a(n) for n=0..54.

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-5,0,2).

Formula

a(n) = n*(1 - (n mod 2))/2 + 2^((n-1)/2)*(n mod 2).

a(n) = n/2 + (2^((n-1)/2) - n/2)*(n mod 2).

a(n) = 4*a(n-2) - 5*a(n-4) + 2*a(n-6) for n > 5.

G.f.: x*(1 + x - 2*x^2 - 2*x^3 + x^4)/((1 - x^2)^2*(1 - 2*x^2)).

E.g.f.: (x*sinh(x) + sqrt(2)*sinh(sqrt(2)*x))/2.

a(n) = A138219(n)/2.

a(n) = 2^m if n is odd and a(n) = floor(n/2) otherwise. - Chai Wah Wu, Jan 05 2026

Mathematica

a[n_]:=n/2+(2^((n-1)/2)-n/2)Mod[n, 2]; Array[a, 55, 0]

Prog

(Python)
def A390532(n): return 1<<(n>>1) if n&1 else n>>1  # Chai Wah Wu, Jan 05 2026

Crossrefs

Cf. A000079, A001477, A138219.

Sequence in context: A285620 A185959 A006799 * A056429 A133806 A360241

Adjacent sequences: A390529 A390530 A390531 * A390533 A390534 A390535

Keyword

nonn,easy

Author

Stefano Spezia, Jan 04 2026

Status

approved