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 A366013 #29 Dec 19 2024 11:45:36 %S A366013 1,1,10,1,11,1,12,19,1,5,18,25,1,5,18,29,1,5,16,23,33,1,4,6,21,30,37, %T A366013 1,5,8,20,31,33,1,4,9,11,26,38,44,1,3,8,9,20,30,44,48,1,3,4,9,16,27, %U A366013 37,44,49,1,3,4,10,17,25,37,43,48,1,3,4,10,18,22,31,42,47 %N A366013 Irregular triangle read by rows where each row lists coin denominations which make amounts 1 to 99 using the smallest total number of coins. %C A366013 A row of length d makes amounts 1 to 99 using a total of A339333(99,d) coins, which is the minimum possible for d denominations. %C A366013 Denominations within a row are in ascending order and rows are ordered by length and then lexicographically. %C A366013 Each row starts with denomination 1 since 1 is the only way to make amount 1. %C A366013 This is a finite sequence, ending with a row of all denominations 1 to 99 which make all amounts using a single coin each. %C A366013 Amounts 1 to 99 are based on making change in a decimal currency which uses coins for 1 to 99 cents, and notes for whole dollar parts. %C A366013 Minimizing the total number of coins minimizes the average number of coins given as change, assuming each of 1 to 99 are equally likely amounts to be given. %H A366013 Kevin Ryde, <a href="/A366013/b366013.txt">Table of n, a(n) for rows 1..600 (lengths d=1..16 and some d=17), flattened</a> %H A366013 Kevin Ryde, <a href="/A366013/a366013_1.c.txt">C Code</a> %H A366013 Jeffrey Shallit, <a href="http://dx.doi.org/10.1007/BF02984830">What This Country Needs is an 18ยข Piece</a>, The Mathematical Intelligencer, 25-2, pages 20-23, 2003, figure 1 rows to d=7, and also <a href="https://cs.uwaterloo.ca/~shallit/Papers/change2.pdf">author's copy</a>, 2002. %H A366013 Thomas Young, <a href="/A364607/a364607_2.pdf">Change the Dime, not the Dollar</a>, 1995, first set of denominations d=4 (see A364607). %e A366013 Triangle begins: %e A366013 k=1 2 3 4 5 6 %e A366013 n=1: 1 %e A366013 n=2: 1, 10 %e A366013 n=3: 1, 11 %e A366013 n=4: 1, 12, 19 %e A366013 n=5: 1, 5, 18, 25 %e A366013 n=6: 1, 5, 18, 29 %e A366013 n=7: 1, 5, 16, 23, 33 %e A366013 n=8: 1, 4, 6, 21, 30, 37 %e A366013 n=9: 1, 5, 8, 20, 31, 33 %e A366013 Rows n=5 and n=6 are of length d=4 and are the two sets of denominations which can make amounts 1 to 99 using the minimum total of A339333(99,4) = 389 coins. %o A366013 (C) /* See links */ %Y A366013 Cf. A339333, A364607 (row n=5). %K A366013 nonn,tabf,fini %O A366013 1,3 %A A366013 _Kevin Ryde_, Sep 28 2023