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.
%I A240437 #48 Jul 04 2023 11:40:49
%S A240437 0,20,100,600,3000,15500,77500,390000,1950000,9762500,48812500,
%T A240437 244125000,1220625000,6103437500,30517187500,152587500000,
%U A240437 762937500000,3814695312500,19073476562500,95367421875000,476837109375000,2384185742187500,11920928710937500,59604644531250000,298023222656250000
%N A240437 Number of non-palindromic n-tuples of 5 distinct elements.
%H A240437 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5, 5, -25).
%F A240437 a(n) = 1/2 * 5^(n/2) * ((sqrt(5)-1) * (-1)^n - sqrt(5)-1) + 5^n.
%F A240437 a(n) = 5^n - 5^ceiling(n/2).
%F A240437 a(n) = A000351(n) - A056451(n).
%F A240437 G.f.: (20*x^2) / (1 - 5*x - 5*x^2 + 25*x^3). [corrected by _Peter Luschny_, May 13 2019]
%e A240437 For n=3 a(3)=100 solutions are:
%e A240437 {0,0,1}, {0,0,2}, {0,0,3}, {0,0,4}, {0,1,1}, {0,1,2}, {0,1,3}, {0,1,4},
%e A240437 {0,2,1}, {0,2,2}, {0,2,3}, {0,2,4}, {0,3,1}, {0,3,2}, {0,3,3}, {0,3,4},
%e A240437 {0,4,1}, {0,4,2}, {0,4,3}, {0,4,4}, {1,0,0}, {1,0,2}, {1,0,3}, {1,0,4},
%e A240437 {1,1,0}, {1,1,2}, {1,1,3}, {1,1,4}, {1,2,0}, {1,2,2}, {1,2,3}, {1,2,4},
%e A240437 {1,3,0}, {1,3,2}, {1,3,3}, {1,3,4}, {1,4,0}, {1,4,2}, {1,4,3}, {1,4,4},
%e A240437 {2,0,0}, {2,0,1}, {2,0,3}, {2,0,4}, {2,1,0}, {2,1,1}, {2,1,3}, {2,1,4},
%e A240437 {2,2,0}, {2,2,1}, {2,2,3}, {2,2,4}, {2,3,0}, {2,3,1}, {2,3,3}, {2,3,4},
%e A240437 {2,4,0}, {2,4,1}, {2,4,3}, {2,4,4}, {3,0,0}, {3,0,1}, {3,0,2}, {3,0,4},
%e A240437 {3,1,0}, {3,1,1}, {3,1,2}, {3,1,4}, {3,2,0}, {3,2,1}, {3,2,2}, {3,2,4},
%e A240437 {3,3,0}, {3,3,1}, {3,3,2}, {3,3,4}, {3,4,0}, {3,4,1}, {3,4,2}, {3,4,4},
%e A240437 {4,0,0}, {4,0,1}, {4,0,2}, {4,0,3}, {4,1,0}, {4,1,1}, {4,1,2}, {4,1,3},
%e A240437 {4,2,0}, {4,2,1}, {4,2,2}, {4,2,3}, {4,3,0}, {4,3,1}, {4,3,2}, {4,3,3},
%e A240437 {4,4,0}, {4,4,1}, {4,4,2}, {4,4,3}.
%p A240437 gf := (20*x^2) / (1 - 5*x - 5*x^2 + 25*x^3): ser := series(gf, x, 26):
%p A240437 seq(coeff(ser,x,n), n=1..25); # _Peter Luschny_, May 13 2019
%t A240437 Table[1/2 * 5^(n/2) * ((Sqrt[5]-1) * (-1)^n - Sqrt[5]-1) + 5^n, {n, 25}]
%o A240437 (PARI) concat([0], Vec( ( (20*x^2) / (1 - 5*x - 5*x^2 + 25*x^3) + O(x^30) ) ) ) \\ _Joerg Arndt_, Aug 18 2014
%Y A240437 Cf. A233411, A242026, A242278.
%K A240437 nonn,easy
%O A240437 1,2
%A A240437 _Mikk Heidemaa_, Aug 17 2014