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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 14 19:27 EST 2019. Contains 329987 sequences. (Running on oeis4.)