A089197 -id:A089197 - cp's OEIS frontend

A245588 The minimal number of coins needed to make change for n units in a currency system with coins of value 1,2,5,13,34,89,...,Fibonacci(2k-1).

0, 1, 1, 2, 2, 1, 2, 2, 3, 3, 2, 3, 3, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 3, 4, 4, 2, 3, 3, 4, 4, 3, 4, 4, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 3, 4, 4, 2, 3, 3, 4, 4, 3, 4, 4, 5, 5, 4, 5, 5, 3, 4, 4, 5, 5, 4, 5, 5, 2, 3, 3, 4, 4, 3, 4, 4, 5, 5, 4, 5, 5, 3, 4, 4, 5, 5, 4, 5, 5, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 3, 4, 4, 2, 3, 3, 4

Offset: 0

Colin Barker, Jul 26 2014

nonn

			a(12) = 3 because the minimal number of coins needed to make 12 = 2+5+5 is 3.

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Cf. A000045, A089197.

a(0)=0 prepended by Alois P. Heinz, May 26 2015

A103563 Number of partitions of n into even-subscripted Fibonacci numbers (1,3,8,21,55,144,...).

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 23, 26, 27, 29, 32, 33, 36, 39, 40, 43, 46, 48, 51, 54, 57, 60, 64, 67, 70, 75, 78, 81, 87, 90, 94, 100, 103, 108, 114, 118, 124, 130, 135, 141, 147, 153, 159, 167, 174, 180, 189, 196, 202

Offset: 0

Emeric Deutsch, Mar 23 2005

nonn

Euler transform of the characteristic function of the even-subscripted Fibonacci numbers.

			a(8)=4 because we have 8, 3+3+1+1, 3+1+1+1+1+1 and 1+1+1+1+1+1+1+1.

Cf. A001906, A089197.

G.f.=1/product((1-x^fibonacci(2k)), k=1..infinity).

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.

Original entry on oeis.org

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

Christopher Cormier, Jan 14 2016

nonn

			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.

Cf. A000008, A001300, A089197, A208216.

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 *)

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A245588 The minimal number of coins needed to make change for n units in a currency system with coins of value 1,2,5,13,34,89,...,Fibonacci(2k-1).

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A103563 Number of partitions of n into even-subscripted Fibonacci numbers (1,3,8,21,55,144,...).

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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.

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Mathematica