A255831 Square array A(m,n) = Resultant(X^m+n,(X+1)^m+n), read by (falling) antidiagonals, m >= 1, n >= 0.

1, 1, 1, 1, 5, 1, 1, 9, 28, 1, 1, 13, 109, 153, 1, 1, 17, 244, 1617, 3751, 1, 1, 21, 433, 5929, 52501, 175760, 1, 1, 25, 676, 14625, 258751, 3261249, 6835648, 1, 1, 29, 973, 29241, 810001, 19763200, 148756357, 1051779953, 1, 1, 33, 1324, 51313, 1968751, 73559825, 1086478912, 23937893793, 364668913756, 1

Offset

0,5

Comments

This polynomial resultant gives the period for solutions to the equations A255852 - A255869. For example, A010034(n) = A255859(17) + A(17,9)*(n-1). In general, there may be more than one starting solutions (cf. A118119).

Links

Table of n, a(n) for n=0..54.

Example

The square array starts at its upper left as follows:
[ 1      1       1        1        1         1         1 ... ]
[ 1      5       9       13       17        21        25 ... ]
[ 1     28     109      244      433       676       973 ... ]
[ 1    153    1617     5929    14625     29241     51313 ... ]
[ 1   3751   52501   258751   810001   1968751   4072501 ... ]
[ 1 175760 3261249 19763200 73559825 207499536 488999665 ... ]
[ :     :       :        :        :         :         :  ·.  ]
[ :     :       :        :        :         :         :    ·.]

Prog

(PARI) A255831(m, n)=polresultant('x^m+n, ('x+1)^m+n)
(Python)
from sympy import resultant
from sympy.abc import x
def A255831_T(m, n): return resultant(x**m+n, (x+1)**m+n) # Chai Wah Wu, May 08 2024

Crossrefs

Sequence in context: A184883 A279003 A210651 * A363970 A356113 A188461

Adjacent sequences: A255828 A255829 A255830 * A255832 A255833 A255834

Keyword

nonn,tabl

Author

M. F. Hasler, Mar 17 2015

Extensions

Edited by Max Alekseyev, Aug 07 2015

Status

approved