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 A309997 #18 Aug 12 2022 10:16:39 %S A309997 1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,2,2,1,1,2,2,2,2,1,1,1,1,2,2,1,1, %T A309997 1,1,1,1,2,2,1,1,2,2,1,1,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,2,2,1,1,2,2, %U A309997 1,1,2,2,1,1,1,1,1,1,2,2,2,2,1,1,2,2,2 %N A309997 Number of paths from 2 to n of length A307092(n) - 1 via maps of the form x -> x + x^j, where j is a nonnegative integer. %C A309997 This sequence counts paths starting from 2 since there are an infinite number of maps from 1 to 2 via 1 -> 1 + 1^j. %C A309997 Records occur at 2, 12, 226, 372, 744, 1490, 139511, ... %H A309997 Peter Kagey, <a href="/A309997/b309997.txt">Table of n, a(n) for n = 2..10000</a> %H A309997 Peter Kagey, <a href="https://codegolf.stackexchange.com/q/190877/53884">Count the number of paths to n</a>, Code Golf Stack Exchange. %e A309997 For n = 520, the a(520) = 3 sequences of A307092(520)-1 = 3 maps are: %e A309997 2 -> 2 + 2^1 -> 4 + 4^1 -> 8 + 8^3 = 520 %e A309997 2 -> 2 + 2^1 -> 4 + 4^4 -> 260 + 260^1 = 520 %e A309997 2 -> 2 + 2^7 -> 130 + 130^1 -> 260 + 260^1 = 520 %e A309997 With exponents (1,1,3), (1,4,1), and (7,1,1) respectively. %Y A309997 Cf. A307074, A307092. %K A309997 nonn %O A309997 2,11 %A A309997 _Peter Kagey_, Aug 26 2019