This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A303050 #36 Mar 10 2024 19:28:11
%S A303050 9,252,10944,617472,41457024,3141499392,259346018304,22749987520512,
%T A303050 2082519895670784,196336888097144832,18885576885968830464,
%U A303050 1841197721072909156352,181107406524439376953344,17918621160090649673859072,1779590652288735614991335424
%N A303050 Number of 2n-digit decimal numbers without leading zeros where each digit appears an even number of times.
%H A303050 T. V. Raziman, <a href="/A303050/b303050.txt">Table of n, a(n) for n = 1..30</a>
%H A303050 Quora, <a href="https://www.quora.com/How-many-2n-digit-numbers-are-there-such-that-each-digit-is-repeated-even-possibly-0-times-n-is-a-natural-number#"> How many 2n digit numbers are there such that each digit is repeated even (possibly 0) times?</a>
%H A303050 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (220,-16368,489280,-5395456,14745600).
%F A303050 a(n) = 9/10 * 1/(2^10) * (2 * 10^(2n) + 20 * 8^(2n) + 90 * 6^(2n) + 240 * 4^(2n) + 420 * 2^(2n)) (proved in the Quora answers).
%F A303050 G.f.: -9 *(1111680*x^4 -229888*x^3 +11424*x^2 -192*x +1) *x / ((100*x-1) *(4*x-1) *(36*x-1) *(64*x-1) *(16*x-1)). - _Alois P. Heinz_, Apr 17 2018
%e A303050 For n=1, the a(1)=9 numbers are 11, 22, 33, ..., 88, 99.
%e A303050 For n=2, the a(2)=252 numbers are 1001, 1010, 1100, 1111, 1122, 1212, 1221, ..., 9988, 9999.
%t A303050 LinearRecurrence[{220, -16368, 489280, -5395456, 14745600}, {9, 252, 10944, 617472, 41457024}, 20] (* _Paolo Xausa_, Mar 10 2024 *)
%K A303050 nonn,base,easy
%O A303050 1,1
%A A303050 _T. V. Raziman_, Apr 17 2018