login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A157155 Triangle T(n, k, m) = (m*(n-k) + 1)*T(n-1, k-1, m) + (m*k + 1)*T(n-1, k, m) - m*k*(n-k)*T(n-2, k-1, m) with T(n, 0, m) = T(n, n, m) = 1 and m = 4, read by rows. 23
1, 1, 1, 1, 6, 1, 1, 31, 31, 1, 1, 156, 462, 156, 1, 1, 781, 5442, 5442, 781, 1, 1, 3906, 57263, 124860, 57263, 3906, 1, 1, 19531, 566153, 2335435, 2335435, 566153, 19531, 1, 1, 97656, 5396164, 38814088, 71413750, 38814088, 5396164, 97656, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
T(n, k, m) = (m*(n-k) + 1)*T(n-1, k-1, m) + (m*k + 1)*T(n-1, k, m) - m*k*(n-k)*T(n-2, k-1, m) with T(n, 0, m) = T(n, n, m) = 1 and m = 4.
T(n, n-k, m) = T(n, k, m).
T(n, 1, 4) = A003463(n). - G. C. Greubel, Jan 10 2022
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 6, 1;
1, 31, 31, 1;
1, 156, 462, 156, 1;
1, 781, 5442, 5442, 781, 1;
1, 3906, 57263, 124860, 57263, 3906, 1;
1, 19531, 566153, 2335435, 2335435, 566153, 19531, 1;
1, 97656, 5396164, 38814088, 71413750, 38814088, 5396164, 97656, 1;
MATHEMATICA
T[n_, k_, m_]:= T[n, k, m]= If[k==0 || k==n, 1, (m*(n-k)+1)*T[n-1, k-1, m] + (m*k+1)*T[n-1, k, m] - m*k*(n-k)*T[n-2, k-1, m]];
Table[T[n, k, 4], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jan 10 2022 *)
PROG
(Sage)
@CachedFunction
def T(n, k, m): # A157155
if (k==0 or k==n): return 1
else: return (m*(n-k) +1)*T(n-1, k-1, m) + (m*k+1)*T(n-1, k, m) - m*k*(n-k)*T(n-2, k-1, m)
flatten([[T(n, k, 4) for k in (0..n)] for n in (0..20)]) # G. C. Greubel, Jan 10 2022
CROSSREFS
Cf. A007318 (m=0), A157152 (m=1), A157153 (m=2), A157154 (m=3), this sequence (m=4), A157156 (m=5).
Cf. A003463.
Sequence in context: A111578 A166349 A176429 * A022169 A156601 A178232
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Feb 24 2009
EXTENSIONS
Edited by G. C. Greubel, Jan 10 2022
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 15 02:08 EDT 2024. Contains 374323 sequences. (Running on oeis4.)