A371764 Triangle read by rows: Trace of the Akiyama-Tanigawa algorithm for powers x^3.

0, 1, 1, 13, 14, 8, 73, 86, 57, 27, 301, 374, 273, 148, 64, 1081, 1382, 1065, 628, 305, 125, 3613, 4694, 3729, 2308, 1205, 546, 216, 11593, 15206, 12297, 7828, 4265, 2058, 889, 343, 36301, 47894, 39153, 25348, 14165, 7098, 3241, 1352, 512

Offset: 0

Author

Peter Luschny, Apr 15 2024

Keywords

• nonn
• tabl

Comments

See the comments in A371763.

Examples

			Triangle starts:
0:                        0
1:                      1,  1
2:                   13,  14, 8
3:                 73, 86,  57, 27
4:             301, 374, 273, 148, 64
5:        1081, 1382, 1065, 628, 305, 125
6:     3613, 4694, 3729, 2308, 1205, 546, 216
7: 11593, 15206, 12297, 7828, 4265, 2058, 889, 343
		

Crossrefs

Cf. A371761, A371763.

Cf. A006230 (left edge).

Programs

Julia

# Using function ATPtriangle from A371763.
ATPtriangle(3, 8)

Maple

# Using function ATPtriangle from A371763.
ATPtriangle(3, 9);
# Or, after Detlef Meya:
T := (n,k) -> (k+1)*(7-(k+2)*(3*2^(n-k+1)-(k+3)*3^(n-k)))-`if`(n=k,1,0):
seq(seq(T(n, k), k = 0..n), n = 0..8);  # Peter Luschny, Apr 21 2024

Mathematica

T[n_, k_] := If[n==k, n^3, 2*Binomial[k + 3, k]*3^(n - k + 1) - 6*Binomial[k + 2, k]*2^(n - k + 1) + 7*(k + 1)]; Flatten[Table[T[n, k],{n, 0, 8},{k, 0, n}]] (* Detlef Meya, Apr 21 2024 *)

Python

# See function ATPowList in A371761.

Formula

T(n, k) = n^3 if n=k, otherwise 2*binomial(k + 3, k)*3^(n - k + 1) - 6*binomial(k + 2, k)*2^(n - k + 1) + 7*(k + 1). - Detlef Meya, Apr 21 2024