A371764 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

See the comments in A371763.

LINKS

Table of n, a(n) for n=0..44.

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

EXAMPLE

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

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 *)

PROG

(Python) # See function ATPowList in A371761.

(Julia) # Using function ATPtriangle from A371763.

ATPtriangle(3, 8)

CROSSREFS

Cf. A371761, A371763.

Cf. A006230 (left edge).

Sequence in context: A254069 A309990 A196461 * A004502 A020512 A337159

Adjacent sequences: A371761 A371762 A371763 * A371765 A371766 A371767

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Apr 15 2024

STATUS

approved