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A240437 Number of non-palindromic n-tuples of 5 distinct elements. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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Last modified January 20 04:53 EST 2021. Contains 340301 sequences. (Running on oeis4.)