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A056451 Number of palindromes using a maximum of five different symbols. 11
1, 5, 5, 25, 25, 125, 125, 625, 625, 3125, 3125, 15625, 15625, 78125, 78125, 390625, 390625, 1953125, 1953125, 9765625, 9765625, 48828125, 48828125, 244140625, 244140625, 1220703125, 1220703125, 6103515625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of achiral rows of n colors using up to five colors. For a(3) = 25, the rows are AAA, ABA, ACA, ADA, AEA, BAB, BBB, BCB, BDB, BEB, CAC, CBC, CCC, CDC, CEC, DAD, DBD, DCD, DDD, DED, EAE, EBE, ECE, EDE, and EEE. - Robert A. Russell, Nov 09 2018

REFERENCES

M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (0,5).

FORMULA

a(n) = 5^floor((n+1)/2).

a(n) = 5*a(n-2). - Colin Barker, May 06 2012

G.f.: (1+5*x) / (1-5*x^2). - Colin Barker, May 06 2012 [Adapted to offset 0 by Robert A. Russell, Nov 07 2018]

a(n) = C(5,0)*A000007(n) + C(5,1)*A057427(n) + C(5,2)*A056453(n) + C(5,3)*A056454(n) + C(5,4)*A056455(n) + C(5,5)*A056456(n). - Robert A. Russell, Nov 08 2018

MATHEMATICA

LinearRecurrence[{0, 5}, {1, 5}, 30] (* or *) Riffle[5^Range[0, 20], 5^Range[20]] (* Harvey P. Dale, Jul 28 2018 *)

Table[5^Ceiling[n/2], {n, 0, 40}] (* Robert A. Russell, Nov 07 2018 *)

PROG

(MAGMA) [5^Floor((n+1)/2): n in [0..40]]; // Vincenzo Librandi, Aug 16 2011

(PARI) vector(40, n, n--; 5^floor((n+1)/2)) \\ G. C. Greubel, Nov 07 2018

CROSSREFS

Column k=5 of A321391.

Cf. A016116.

Cf. A000351 (oriented), A032122 (unoriented), A032088(n>1) (chiral).

Sequence in context: A227076 A223186 A071340 * A074872 A162962 A170834

Adjacent sequences:  A056448 A056449 A056450 * A056452 A056453 A056454

KEYWORD

nonn,easy

AUTHOR

Marks R. Nester

EXTENSIONS

a(0)=1 prepended by Robert A. Russell, Nov 07 2018

STATUS

approved

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Last modified March 1 03:09 EST 2021. Contains 341732 sequences. (Running on oeis4.)