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

Author

Tanya Khovanova, Aug 30 2009

Keywords

• nonn
• easy

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.

Examples

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

Links

• 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).

Crossrefs

Cf. A056470, A056471, A164864, A188164.

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]