The Recurrence operator annihilating a_r(n):=The number of ways of making change of n cents only using pennies, nickels, dimes, quarters half-dollars and dollar-coins is where the person has r pockets the money can come from, is: 2 3 4 5 6 7 8 9 (-191 r - n) - r N - r N - r N - r N - 6 r N - r N - r N - r N - r N - 10 11 12 13 14 15 16 17 18 16 r N - r N - r N - r N - r N - 6 r N - r N - r N - r N 19 20 21 22 23 24 25 26 - r N - 16 r N - r N - r N - r N - r N - 31 r N - r N - r 27 28 29 30 31 32 33 34 35 N - r N - r N - 16 r N - r N - r N - r N - r N - 6 r N - 36 37 38 39 40 41 42 43 44 r N - r N - r N - r N - 16 r N - r N - r N - r N - r N - 45 46 47 48 49 50 51 52 53 6 r N - r N - r N - r N - r N - 91 r N - r N - r N - r N 54 55 56 57 58 59 60 61 - r N - 6 r N - r N - r N - r N - r N - 16 r N - r N - r 62 63 64 65 66 67 68 69 70 N - r N - r N - 6 r N - r N - r N - r N - r N - 16 r N - 71 72 73 74 75 76 77 78 79 r N - r N - r N - r N - 31 r N - r N - r N - r N - r N - 80 81 82 83 84 85 86 87 88 16 r N - r N - r N - r N - r N - 6 r N - r N - r N - r N 89 90 91 92 93 94 95 96 - r N - 16 r N - r N - r N - r N - r N - 6 r N - r N - r 97 98 99 100 N - r N - r N + (100 + n) N This took, 16.373, seconds