A056470 -id:A056470 - cp's OEIS frontend

A056479 Number of primitive (aperiodic) palindromic structures using a maximum of five different symbols.

1, 1, 0, 1, 1, 4, 3, 14, 13, 50, 47, 201, 196, 854, 840, 3839, 3830, 18001, 17947, 86471, 86419, 421989, 421803, 2079474, 2079260, 10306747, 10305897, 51263890, 51263086, 255514354, 255510460, 1275163904, 1275160060, 6368612099, 6368594300, 31821472593, 31821454413

Offset: 0

Marks R. Nester

nonn

Permuting the symbols will not change the structure.

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]

Andrew Howroyd, Table of n, a(n) for n = 0..500

Cf. A056461, A056470, A284826.

a(n) = Sum_{d|n} mu(d)*A056470(n/d) for n > 0.

a(n) = Sum_{k=1..5} A284826(n, k) for n > 0. - Andrew Howroyd, Oct 02 2019

a(0)=1 prepended and terms a(32) and beyond from Andrew Howroyd, Oct 02 2019

A056506 Number of periodic palindromic structures using a maximum of five different symbols.

Original entry on oeis.org

1, 1, 2, 2, 5, 5, 13, 15, 41, 52, 143, 202, 564, 855, 2433, 3845, 11101, 18002, 52662, 86472, 255128, 422005, 1252898, 2079475, 6197590, 10306752, 30796243, 51263942, 153411664, 255514355, 765393943, 1275163905, 3822001141, 6368612302, 19095317552, 31821472612

Offset: 0

Marks R. Nester

nonn

For example, aaabbb is not a (finite) palindrome but it is a periodic palindrome. Permuting the symbols will not change the structure.

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]

Andrew Howroyd, Table of n, a(n) for n = 0..200

Cf. A056470, A285012.

a(n) = Sum_{k=1..5} A285012(n, k) for n > 0. - Andrew Howroyd, Oct 01 2019

Corrected by T. D. Noe, Oct 25 2006

a(0)=1 prepended and terms a(17) and beyond from Andrew Howroyd, Oct 01 2019

A164904 a(n) is the number of palindromic structures using a maximum of ten different symbols.

Original entry on oeis.org

1, 1, 1, 2, 2, 5, 5, 15, 15, 52, 52, 203, 203, 877, 877, 4140, 4140, 21147, 21147, 115975, 115975, 678569, 678569, 4213530, 4213530, 27641927, 27641927, 190829797, 190829797, 1381367941, 1381367941, 10448276360, 10448276360, 82285618467

Offset: 0

Tanya Khovanova, Aug 30 2009

a(n) is the number of palindromic word structures of length n using 10-ary alphabet.

a(n) is the same as taking every element twice from A164864.

			Four-digit palindromes have two different digits structures: aaaa and abba. Hence a(4)=2.

Index entries for linear recurrences with constant coefficients, signature (1, 45, -45, -861, 861, 9135, -9135, -58674, 58674, 233100, -233100, -557864, 557864, 732960, -732960, -403200, 403200).

Cf. A056470, A056471, A164864, A188164.

G.f.: (148329*x^17 -403200*x^16 -210253*x^15 +732960*x^14 +122692*x^13 -557864*x^12 -38365*x^11 +233100*x^10 +6965*x^9 -58674*x^8 -736*x^7 +9135*x^6 +42*x^5 -861*x^4 -x^3 +45*x^2 -1) / ((x -1)*(2*x -1)*(2*x +1)*(2*x^2 -1)*(3*x^2 -1)*(5*x^2 -1)*(6*x^2 -1)*(7*x^2 -1)*(8*x^2 -1)*(10*x^2 -1)). [Colin Barker, Dec 05 2012]

A188164 Number of palindromic structures of length n.

Original entry on oeis.org

1, 1, 1, 2, 2, 5, 5, 15, 15, 52, 52, 203, 203, 877, 877, 4140, 4140, 21147, 21147, 115975, 115975, 678570, 678570, 4213597, 4213597, 27644437, 27644437, 190899322, 190899322, 1382958545, 1382958545

Offset: 0

Franklin T. Adams-Watters, Mar 23 2011

nonn

Permuting the symbols does not change the structure; so e.g. aba and bab are equivalent.

			For n=4, the 2 structures are aaaa and abba. For n=5, the 5 structures are aaaaa, aabaa, ababa, abbba, and abcba.

Cf. A000110, A056470, A056471, A164904.

a(2n) = a(2n-1) = B(n), where B(n) = A000110(n) are the Bell numbers.

A056474 Number of palindromic structures using exactly five different symbols.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 15, 15, 140, 140, 1050, 1050, 6951, 6951, 42525, 42525, 246730, 246730, 1379400, 1379400, 7508501, 7508501, 40075035, 40075035, 210766920, 210766920, 1096190550

Offset: 1

Marks R. Nester

Permuting the symbols will not change the structure.

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]

Index entries for linear recurrences with constant coefficients, signature (1,14,-14,-71,71,154,-154,-120,120).

Cf. A000481, A056470.

Table[StirlingS2[Floor[(n+1)/2],5],{n,40}] (* Harvey P. Dale, Dec 18 2012 *)

stirling2( [(n+1)/2], 5).

G.f.: -x^9/((x-1)*(2*x-1)*(2*x+1)*(2*x^2-1)*(3*x^2-1)*(5*x^2-1)). [Colin Barker, Jul 24 2012]

cp's OEIS Frontend

A056479 Number of primitive (aperiodic) palindromic structures using a maximum of five different symbols.

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A056506 Number of periodic palindromic structures using a maximum of five different symbols.

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A164904 a(n) is the number of palindromic structures using a maximum of ten different symbols.

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A188164 Number of palindromic structures of length n.

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A056474 Number of palindromic structures using exactly five different symbols.

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