preserver_image / hadamard_multiplier, shift 2
Image under a real-rootedness preserver. All operations
Parameters (20)
- all
- derivative_polynomial, shift 0 422 proof steps, 410 sequences
- euler_polynomial, shift 0 367 proof steps, 352 sequences
- affine, shift 0 333 proof steps, 318 sequences
- reversal, shift 0 169 proof steps, 164 sequences
- mobius, shift 0 160 proof steps, 160 sequences
- hadamard_multiplier, shift 0 5 proof steps, 5 sequences
- affine, shift -1 5 proof steps, 5 sequences
- affine, shift 1 4 proof steps, 4 sequences
- reversal, shift 1 4 proof steps, 4 sequences
- hadamard_multiplier, shift 2 3 proof steps, 3 sequences
- euler_polynomial, shift 1 2 proof steps, 2 sequences
- hadamard_multiplier, shift -1 2 proof steps, 2 sequences
- affine, shift 2 2 proof steps, 2 sequences
- euler_polynomial, shift 2 1 proof steps, 1 sequences
- hadamard_multiplier, shift 1 1 proof steps, 1 sequences
- reversal, shift -1 1 proof steps, 1 sequences
- derivative_of_power_multiple, shift 0 1 proof steps, 1 sequences
- derivative_of_power_multiple, shift 1 1 proof steps, 1 sequences
- derivative_polynomial, shift -1 1 proof steps, 1 sequences
- derivative_polynomial, shift 2 1 proof steps, 1 sequences
3 sequences
-
A108838 → ⊙ C(n+2,k+1) (shift +2)
30, 120, 30 · 60, 600, 600, 60 … row sums 180, 1320, 9660, 70896, 522648, …
-
A352880: Triangle read by rows: T(n,k) = number of vertices of degree k in an origami flip graph OFG(A2n).
A007318 → ⊙ C(n+1,k+1) (shift +2)8 · 12, 18 · 16, 64, 32 · 20, 150, 200, 50 … row sums 8, 30, 112, 420, 1584, 6006, 22880, …
-
A086645 → ⊙ C(n+1,k) (shift +2)
1, 12, 1 · 1, 45, 45, 1 · 1, 112, 420, 112, 1 … row sums 14, 92, 646, 4652, 34124, 253528, …