cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A255831 #15 May 08 2024 14:27:18
%S A255831 1,1,1,1,5,1,1,9,28,1,1,13,109,153,1,1,17,244,1617,3751,1,1,21,433,
%T A255831 5929,52501,175760,1,1,25,676,14625,258751,3261249,6835648,1,1,29,973,
%U A255831 29241,810001,19763200,148756357,1051779953,1,1,33,1324,51313,1968751,73559825,1086478912,23937893793,364668913756,1
%N A255831 Square array A(m,n) = Resultant(X^m+n,(X+1)^m+n), read by (falling) antidiagonals, m >= 1, n >= 0.
%C A255831 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).
%e A255831 The square array starts at its upper left as follows:
%e A255831 [ 1      1       1        1        1         1         1 ... ]
%e A255831 [ 1      5       9       13       17        21        25 ... ]
%e A255831 [ 1     28     109      244      433       676       973 ... ]
%e A255831 [ 1    153    1617     5929    14625     29241     51313 ... ]
%e A255831 [ 1   3751   52501   258751   810001   1968751   4072501 ... ]
%e A255831 [ 1 175760 3261249 19763200 73559825 207499536 488999665 ... ]
%e A255831 [ :     :       :        :        :         :         :  ·.  ]
%e A255831 [ :     :       :        :        :         :         :    ·.]
%o A255831 (PARI) A255831(m,n)=polresultant('x^m+n,('x+1)^m+n)
%o A255831 (Python)
%o A255831 from sympy import resultant
%o A255831 from sympy.abc import x
%o A255831 def A255831_T(m,n): return resultant(x**m+n,(x+1)**m+n) # _Chai Wah Wu_, May 08 2024
%K A255831 nonn,tabl
%O A255831 0,5
%A A255831 _M. F. Hasler_, Mar 17 2015
%E A255831 Edited by _Max Alekseyev_, Aug 07 2015