A375025 Triangle read by rows: Matrix inverse of row-reversed A374439.

1, -2, 1, 3, -2, 1, -4, 2, -2, 1, 6, -2, 1, -2, 1, -10, 5, 0, 0, -2, 1, 15, -10, 5, 2, -1, -2, 1, -20, 10, -12, 6, 4, -2, -2, 1, 30, -8, 4, -16, 8, 6, -3, -2, 1, -52, 26, 8, -4, -22, 11, 8, -4, -2, 1, 78, -60, 30, 30, -15, -30, 15, 10, -5, -2, 1

Offset

0,2

Links

Table of n, a(n) for n=0..65.

Example

Triangle starts:
  [0] [  1]
  [1] [ -2,   1]
  [2] [  3,  -2,   1]
  [3] [ -4,   2,  -2,   1]
  [4] [  6,  -2,   1,  -2,   1]
  [5] [-10,   5,   0,   0,  -2,  1]
  [6] [ 15, -10,   5,   2,  -1, -2,  1]
  [7] [-20,  10, -12,   6,   4, -2, -2,  1]
  [8] [ 30,  -8,   4, -16,   8,  6, -3, -2,  1]
  [9] [-52,  26,   8,  -4, -22, 11,  8, -4, -2, 1]

Maple

A := (n, k) -> ifelse(k::odd, 2, 1)*binomial(n-irem(k, 2)-iquo(k, 2), iquo(k, 2)):
ARevRow := n -> local k; [seq(A(n, n-k), k = 0..n)]:
M := m -> Matrix(m, (n, k) -> ifelse(k > n, 0, ARevRow(n-1)[k])):
T := n -> LinearAlgebra:-MatrixInverse(M(n)): T(11);

Prog

(Python)
from functools import cache
@cache
def Trow(n):
    if n == 0: return [1]
    if n == 1: return [-2, 1]
    fli = Trow(n - 1)
    row = [1] * (n + 1)
    row[n - 1] = -2
    for k in range(n - 2, 0, -1):
        row[k] = fli[k - 1] - fli[k + 1]
    row[0] = -2 * fli[0] - fli[1]
    return row
# Peter Luschny, Aug 18 2024

Crossrefs

Column 0 and row sums: A086990, A090412; alternating row sums: A375026.

Cf. A374439.

Sequence in context: A234575 A294733 A275724 * A381050 A193278 A337632

Adjacent sequences: A375022 A375023 A375024 * A375026 A375027 A375028

Keyword

sign,tabl

Author

Peter Luschny, Aug 07 2024

Status

approved