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 A372844 #19 Dec 27 2024 08:48:54 %S A372844 64,708,9421,148992,2742090,57671104,1365730231,35980443648, %T A372844 1044117402868,33098695234560,1138160856018369,42200676331159552, %U A372844 1678427133899138494,71282668099352051712,3219814814790580711915,154137012617228775849984,7795444201708762192584744,415337944634097426474729472 %N A372844 a(n) is the number of parking functions of order n for which the fourth spot is lucky. %C A372844 A lucky spot is one which is parked in by a car which prefers that spot. %H A372844 Steve Butler, Kimberly Hadaway, Victoria Lenius, Preston Martens, and Marshall Moats, <a href="https://arxiv.org/abs/2412.07873">Lucky cars and lucky spots in parking functions</a>, arXiv:2412.07873 [math.CO], 2024. See p. 10. %F A372844 a(n) = (5/8)*(n+1)^(n-1) - (1/8)*(13*n^2 - 26*n + 9)*(n-3)^(n-3). %e A372844 For clarity, we write parentheses around parking functions. For n = 4, there are a(4) = 64 solutions. An example of a parking function of order 4 with a lucky fourth spot is (1,4,2,2); here, the second car parks in the fourth spot which is its preferred spot. This parking function contributes to our count. A non-example is the parking function (1,2,1,2); here, the last car parks in the fourth spot, but its preference is spot 2. This parking function does not contribute to our count. %t A372844 a[n_]:=(5/8)*(n+1)^(n-1)-(1/8)*(13*n^2-26*n+9)*(n-3)^(n-3); Array[a,19,4] (* _Stefano Spezia_, Jun 26 2024 *) %o A372844 (Python) %o A372844 def A372844(n): return 5*(n+1)**(n-1)-(13*(n-1)**2-4)*(n-3)**(n-3)>>3 # _Chai Wah Wu_, Jun 26 2024 %Y A372844 Cf. A000272 (for first spot), A372842 (for second spot), A372843 (for third spot), and A372845 (for fifth spot). %K A372844 nonn %O A372844 4,1 %A A372844 _Kimberly P. Hadaway_, Jun 26 2024