A095090 Number of 4k+3 integers in range ]2^n,2^(n+1)] whose Jacobi-vector is a Motzkin-path (A095100).

1, 1, 2, 3, 6, 9, 17, 33, 60, 108, 202, 360, 703, 1328, 2519, 4779, 9103, 17501, 33473, 64761

Offset: 1

Author

Antti Karttunen and Jun 01 2004

Keywords

• nonn
• more

Links

• A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Crossrefs

Cf. A095092, A095100.

Programs

PARI

is(m) = {my(s=0); for(i=1, m-1, if((s+=kronecker(i, m))<0, return(0))); 1; }
a(n) = {my(c=0); forstep(m=2^n+3-(n==1), 2^(n+1), 4, c+=is(m)); c; } \\ Jinyuan Wang, Jul 20 2020

Formula

a(n) = 2^(n-2) - A095091(n) for n > 1.