A352988 Matrix inverse of triangle A352650.

1, 0, 1, -1, -1, 1, 0, -2, -2, 1, 0, 0, -3, -3, 1, 0, 0, 0, -4, -4, 1, 0, 0, 0, 0, -5, -5, 1, 0, 0, 0, 0, 0, -6, -6, 1, 0, 0, 0, 0, 0, 0, -7, -7, 1, 0, 0, 0, 0, 0, 0, 0, -8, -8, 1, 0, 0, 0, 0, 0, 0, 0, 0, -9, -9, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -10, 1

Offset

0,8

Links

Table of n, a(n) for n=0..77.

Formula

T(n,n) = 1 for n >= 0, and T(n,n-1) = 1 - n for n > 0, and T(n,n-2) = 1 - n for n > 1, and T(n,k) = 0 if n < 0 or k < 0 or n < k or n > k+2.

G.f.: Sum_{n>=0, k=0..n} T(n,k) * x^k * t^n = (1 + t) * (1 - (1 + x) * t) / (1 - x * t)^2.

Alt. row sums equal (-1)^n for n >= 0.

Matrix product with A094587 yields A097806.

Example

The triangle T(n,k) for 0 <= k <= n starts:
n\k :   0    1    2    3    4    5    6    7    8    9
======================================================
  0 :   1
  1 :   0    1
  2 :  -1   -1    1
  3 :   0   -2   -2    1
  4 :   0    0   -3   -3    1
  5 :   0    0    0   -4   -4    1
  6 :   0    0    0    0   -5   -5    1
  7 :   0    0    0    0    0   -6   -6    1
  8 :   0    0    0    0    0    0   -7   -7    1
  9 :   0    0    0    0    0    0    0   -8   -8    1
  etc.

Crossrefs

Cf. A094587, A097806, A352650.

Sequence in context: A258277 A122865 A246656 * A334493 A074080 A359440

Adjacent sequences: A352985 A352986 A352987 * A352989 A352990 A352991

Keyword

sign,easy,tabl

Author

Werner Schulte, Apr 13 2022

Status

approved