A331520 a(0) = a(1) = 1; a(n+2) = Sum_{k=0..n} (binomial(n,k) mod 2) * a(k).

1, 1, 1, 2, 2, 5, 3, 9, 7, 24, 8, 33, 17, 77, 27, 134, 66, 351, 67, 419, 135, 908, 204, 1469, 479, 3643, 553, 4572, 1182, 10227, 1889, 17125, 4641, 43640, 4642, 48283, 9285, 101211, 13929, 158786, 32504, 384441, 37153, 465259, 78957, 1020640, 125414, 1675453

Offset: 0

Author

Ilya Gutkovskiy, Jan 19 2020

Keywords

• nonn

Comments

Shifts 2 places left under the modulo 2 binomial transform.

Crossrefs

Cf. A007476, A010060, A047999, A166966.

Programs

Mathematica

a[0] = a[1] = 1; a[n_] := a[n] = Sum[Mod[Binomial[n - 2, k], 2] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 47}]

Formula

a(n) = Sum_{k=0..n} (-1)^A010060(n-k) * (binomial(n, k) mod 2) * a(k+2).