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A174140
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Numbers congruent to k mod 25, where 10 <= k <= 24.
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4
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10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 110, 111, 112, 113, 114, 115, 116
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OFFSET
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1,1
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COMMENTS
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Numbers whose partition into parts of sizes 1, 5, 10, and 25 having a minimal number of parts includes at least one part of size 10.
For each number the partition is unique.
Amounts in cents requiring at least one dime when the minimal number of coins is selected from pennies, nickels, dimes, and quarters (whether usage of bills for whole-dollar amounts is permitted or not).
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
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FORMULA
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a(n+15) = a(n) + 25 for n >= 1.
G.f.: x*(10 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12 + x^13 + x^14 + x^15) / ((1 - x)^2*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)*(1 - x + x^3 - x^4 + x^5 - x^7 + x^8)).
a(n) = a(n-1) + a(n-15) - a(n-16) for n>16.
(End)
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MATHEMATICA
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Flatten[Table[Range[10, 24]+25n, {n, 0, 5}]] (* Harvey P. Dale, Jun 12 2012 *)
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PROG
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(PARI) Vec(x*(10 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12 + x^13 + x^14 + x^15) / ((1 - x)^2*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)*(1 - x + x^3 - x^4 + x^5 - x^7 + x^8)) + O(x^60)) \\ Colin Barker, Oct 25 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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