A240437 Number of non-palindromic n-tuples of 5 distinct elements.

0, 20, 100, 600, 3000, 15500, 77500, 390000, 1950000, 9762500, 48812500, 244125000, 1220625000, 6103437500, 30517187500, 152587500000, 762937500000, 3814695312500, 19073476562500, 95367421875000, 476837109375000, 2384185742187500, 11920928710937500, 59604644531250000, 298023222656250000

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Index entries for linear recurrences with constant coefficients, signature (5, 5, -25).

Formula

a(n) = 1/2 * 5^(n/2) * ((sqrt(5)-1) * (-1)^n - sqrt(5)-1) + 5^n.

a(n) = 5^n - 5^ceiling(n/2).

a(n) = A000351(n) - A056451(n).

G.f.: (20*x^2) / (1 - 5*x - 5*x^2 + 25*x^3). [corrected by Peter Luschny, May 13 2019]

Example

For n=3 a(3)=100 solutions are:
{0,0,1}, {0,0,2}, {0,0,3}, {0,0,4}, {0,1,1}, {0,1,2}, {0,1,3}, {0,1,4},
{0,2,1}, {0,2,2}, {0,2,3}, {0,2,4}, {0,3,1}, {0,3,2}, {0,3,3}, {0,3,4},
{0,4,1}, {0,4,2}, {0,4,3}, {0,4,4}, {1,0,0}, {1,0,2}, {1,0,3}, {1,0,4},
{1,1,0}, {1,1,2}, {1,1,3}, {1,1,4}, {1,2,0}, {1,2,2}, {1,2,3}, {1,2,4},
{1,3,0}, {1,3,2}, {1,3,3}, {1,3,4}, {1,4,0}, {1,4,2}, {1,4,3}, {1,4,4},
{2,0,0}, {2,0,1}, {2,0,3}, {2,0,4}, {2,1,0}, {2,1,1}, {2,1,3}, {2,1,4},
{2,2,0}, {2,2,1}, {2,2,3}, {2,2,4}, {2,3,0}, {2,3,1}, {2,3,3}, {2,3,4},
{2,4,0}, {2,4,1}, {2,4,3}, {2,4,4}, {3,0,0}, {3,0,1}, {3,0,2}, {3,0,4},
{3,1,0}, {3,1,1}, {3,1,2}, {3,1,4}, {3,2,0}, {3,2,1}, {3,2,2}, {3,2,4},
{3,3,0}, {3,3,1}, {3,3,2}, {3,3,4}, {3,4,0}, {3,4,1}, {3,4,2}, {3,4,4},
{4,0,0}, {4,0,1}, {4,0,2}, {4,0,3}, {4,1,0}, {4,1,1}, {4,1,2}, {4,1,3},
{4,2,0}, {4,2,1}, {4,2,2}, {4,2,3}, {4,3,0}, {4,3,1}, {4,3,2}, {4,3,3},
{4,4,0}, {4,4,1}, {4,4,2}, {4,4,3}.

Maple

gf := (20*x^2) / (1 - 5*x - 5*x^2 + 25*x^3): ser := series(gf, x, 26):
seq(coeff(ser, x, n), n=1..25); # Peter Luschny, May 13 2019

Mathematica

Table[1/2 * 5^(n/2) * ((Sqrt[5]-1) * (-1)^n - Sqrt[5]-1) + 5^n, {n, 25}]

Prog

(PARI) concat([0], Vec( ( (20*x^2) / (1 - 5*x - 5*x^2 + 25*x^3) + O(x^30) ) ) ) \\ Joerg Arndt, Aug 18 2014

Crossrefs

Cf. A233411, A242026, A242278.

Sequence in context: A294112 A188050 A027986 * A174078 A239857 A041772

Adjacent sequences: A240434 A240435 A240436 * A240438 A240439 A240440

Keyword

nonn,easy

Author

Mikk Heidemaa, Aug 17 2014

Status

approved