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.

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

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