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 = 4.
From G. C. Greubel, Mar 03 2022: (Start)
T(n, n-k) = T(n, k).
T(n, 2) = 2^(n+1) - (n+5).
T(n, 3) = (1/2)*( n^2 + 9*n + 16 - 2^(n+2)*(n+3) + 142*3^(n-3) ). (End)
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 8, 1;
1, 23, 23, 1;
1, 54, 170, 54, 1;
1, 117, 818, 818, 117, 1;
1, 244, 3255, 7224, 3255, 244, 1;
1, 499, 11697, 48443, 48443, 11697, 499, 1;
1, 1010, 39560, 276974, 513326, 276974, 39560, 1010, 1;
1, 2033, 128756, 1431604, 4422246, 4422246, 1431604, 128756, 2033, 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, 4], {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 A144436(n, k): return T(n, k, 1, 4)
flatten([[A144436(n, k) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Mar 03 2022
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula and Gary W. Adamson, Oct 04 2008
EXTENSIONS
Edited by G. C. Greubel, Mar 03 2022
STATUS
approved