A367087 Number of solutions to +- 1 +- 3 +- 5 +- 7 +- ... +- (2*n-1) = 0 or 1.

1, 1, 0, 1, 2, 2, 2, 5, 8, 13, 20, 38, 68, 118, 206, 380, 692, 1262, 2306, 4277, 7930, 14745, 27492, 51541, 96792, 182182, 343670, 650095, 1231932, 2338706, 4447510, 8472697, 16164914, 30884150, 59086618, 113189168, 217091832, 416839177, 801247614, 1541726967, 2969432270

Offset: 0

Author

Ilya Gutkovskiy, Jan 26 2024

Keywords

• nonn

Crossrefs

Cf. A005408, A025591, A156700, A292476.

Programs

Maple

b:= proc(n, i) option remember; `if`(n>i^2, 0,
      `if`(i=0, 1, b(n+2*i-1, i-1)+b(abs(n-2*i+1), i-1)))
    end:
a:=n-> b(irem(n, 2), n):
seq(a(n), n=0..40);  # Alois P. Heinz, Jan 26 2024

Mathematica

b[n_, i_] := b[n, i] = If[n > i^2, 0,
   If[i == 0, 1, b[n+2*i-1, i-1] + b[Abs[n-2*i+1], i-1]]];
a[n_] := b[Mod[n, 2], n];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 03 2025, after Alois P. Heinz *)