# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a267419 Showing 1-1 of 1 %I A267419 #32 Feb 21 2016 19:42:52 %S A267419 1,2,2,3,5,8,10,14,17,23,28,35,43,53,64,78,93,112,132,158,184,217,253, %T A267419 295,342,396,455,526,600,689,784,893,1014,1150,1299,1468,1651,1860, %U A267419 2084,2339,2613,2921,3257,3628,4034,4482,4967,5508,6087,6731,7426,8188,9017,9920,10898,11969,13120,14382,15737,17215 %N A267419 Number of ways of making change for n cents using coins whose values are the previous terms in the sequence, starting with 1,2 cents. %e A267419 For n=4, the coins available are 1,2. There are a(4)=3 ways to make 4 cents with these coins: %e A267419 4 = 1+1+1+1 %e A267419 4 = 2+1+1 %e A267419 4 = 2+2 %e A267419 Since there are 3 ways, now the available coins are 1,2,3. For n=5, we have: %e A267419 5 = 1+1+1+1+1 %e A267419 5 = 2+1+1+1 %e A267419 5 = 2+2+1 %e A267419 5 = 3+1+1 %e A267419 5 = 3+2 %e A267419 for 5 ways to make change, so now 1,2,3,5 are available, etc. %t A267419 a = {1, 2}; Do[AppendTo[a, Count[IntegerPartitions@ n, w_ /; AllTrue[w, MemberQ[a, #] &]]], {n, 3, 60}]; a (* _Michael De Vlieger_, Jan 15 2016, Version 10 *) %Y A267419 Cf. A000008, A001300, A089197, A208216. %K A267419 nonn %O A267419 1,2 %A A267419 _Christopher Cormier_, Jan 14 2016 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE