

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.


0



1, 2, 2, 3, 5, 8, 10, 14, 17, 23, 28, 35, 43, 53, 64, 78, 93, 112, 132, 158, 184, 217, 253, 295, 342, 396, 455, 526, 600, 689, 784, 893, 1014, 1150, 1299, 1468, 1651, 1860, 2084, 2339, 2613, 2921, 3257, 3628, 4034, 4482, 4967, 5508, 6087, 6731, 7426, 8188, 9017, 9920, 10898, 11969, 13120, 14382, 15737, 17215
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..60.


EXAMPLE

For n=4, the coins available are 1,2. There are a(4)=3 ways to make 4 cents with these coins:
4 = 1+1+1+1
4 = 2+1+1
4 = 2+2
Since there are 3 ways, now the available coins are 1,2,3. For n=5, we have:
5 = 1+1+1+1+1
5 = 2+1+1+1
5 = 2+2+1
5 = 3+1+1
5 = 3+2
for 5 ways to make change, so now 1,2,3,5 are available, etc.


MATHEMATICA

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 *)


CROSSREFS

Cf. A000008, A001300, A089197, A208216.
Sequence in context: A157176 A276429 A111181 * A076777 A240210 A111123
Adjacent sequences: A267416 A267417 A267418 * A267420 A267421 A267422


KEYWORD

nonn


AUTHOR

Christopher Cormier, Jan 14 2016


STATUS

approved



