A164904 - OEIS

%I #18 Mar 24 2024 08:00:56

%S 1,1,1,2,2,5,5,15,15,52,52,203,203,877,877,4140,4140,21147,21147,

%T 115975,115975,678569,678569,4213530,4213530,27641927,27641927,

%U 190829797,190829797,1381367941,1381367941,10448276360,10448276360,82285618467

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

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

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

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (1, 45, -45, -861, 861, 9135, -9135, -58674, 58674, 233100, -233100, -557864, 557864, 732960, -732960, -403200, 403200).

%F 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]

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

%Y Cf. A056470, A056471, A164864, A188164.

%K nonn,easy

%O 0,4

%A _Tanya Khovanova_, Aug 30 2009