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

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

0,4

Comments

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.

Links

Table of n, a(n) for n=0..33.

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).

Formula

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]

Example

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

Crossrefs

Cf. A056470, A056471, A164864, A188164.

Sequence in context: A055879 A056470 A056471 * A188164 A245846 A245847

Adjacent sequences: A164901 A164902 A164903 * A164905 A164906 A164907

Keyword

nonn,easy

Author

Tanya Khovanova, Aug 30 2009

Status

approved