OFFSET
1,5
LINKS
G. C. Greubel, Rows n = 1..50 of the triangle, flattened
FORMULA
T(n, k) = (m*(n-k) + 1)*T(n-1, k-1) + (m*(k-1) + 1)*T(n-1, k) + j*T(n-2, k-1), where T(n, 1) = T(n, n) = 1, m = -1, and j = 2.
From G. C. Greubel, Mar 03 2022: (Start)
T(n, n-k) = T(n, k).
T(n, 2) = 5 - n, n >= 3.
T(n, 3) = (1/2)*(n^2 - 11*n + 32) - (-1)^n, n >= 4.
T(n, 4) = (1/12)*(-2*n^3 + 36*n^2 - 226*n + 496 - (-1)^n*(2^n - 12*(n-1))), n >= 5. (End)
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 2, 1;
1, 1, 1, 1;
1, 0, 2, 0, 1;
1, -1, 0, 0, -1, 1;
1, -2, 3, 4, 3, -2, 1;
1, -3, 3, -17, -17, 3, -3, 1;
1, -4, 8, 28, 110, 28, 8, -4, 1;
1, -5, 10, -90, -476, -476, -90, 10, -5, 1;
MATHEMATICA
T[n_, k_, m_, j_]:= T[n, k, m, j]= If[k==1 || k==n, 1, (m*(n-k)+1)*T[n-1, k-1, m, j] + (m*(k-1)+1)*T[n-1, k, m, j] + j*T[n-2, k-1, m, j] ];
Table[T[n, k, -1, 2], {n, 15}, {k, n}]//Flatten (* modified by G. C. Greubel, Mar 03 2022 *)
PROG
(Sage)
def T(n, k, m, j):
if (k==1 or k==n): return 1
else: return (m*(n-k)+1)*T(n-1, k-1, m, j) + (m*(k-1)+1)*T(n-1, k, m, j) + j*T(n-2, k-1, m, j)
def A144435(n, k): return T(n, k, -1, 2)
flatten([[A144435(n, k) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Mar 03 2022
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Roger L. Bagula and Gary W. Adamson, Oct 04 2008
EXTENSIONS
Edited by G. C. Greubel, Mar 03 2022
STATUS
approved