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A001304
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Expansion of 1/((1-x)^2*(1-x^2)*(1-x^5)).
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5
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1, 2, 4, 6, 9, 13, 18, 24, 31, 39, 49, 60, 73, 87, 103, 121, 141, 163, 187, 213, 242, 273, 307, 343, 382, 424, 469, 517, 568, 622, 680, 741, 806, 874, 946, 1022, 1102, 1186, 1274, 1366, 1463, 1564, 1670, 1780, 1895, 2015, 2140, 2270, 2405, 2545, 2691, 2842
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OFFSET
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0,2
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COMMENTS
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Ways of making change for n cents using coins of 1, 2 and 5 cents, if two different kinds of 1-cent coin are counted as different. - Matthew Vandermast, Feb 27 2003
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 113, Example (2), D(n; 1,2,4,10).
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LINKS
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FORMULA
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G.f.: 1/((1-x)^2*(1-x^2)*(1-x^5)) = 1 / ((1+x)*(x^4+x^3+x^2+x+1)*(x-1)^4).
a(n) = floor((n+8)*(2*n^2+11*n+18)/120). - Tani Akinari, May 14 2014
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MAPLE
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a:= proc(n) local m, r; m:= iquo(n, 10, 'r'); r:= r+1; (53+ (135+ 100*m) *m) *m/6+ [1, 2, 4, 6, 9, 13, 18, 24, 31, 39][r]+ [0, 5, 11, 18, 26, 35, 45, 56, 68, 81][r]*m+ (r-1)*5 *m^2 end: seq(a(n), n=0..100); # Alois P. Heinz, Oct 05 2008
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MATHEMATICA
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CoefficientList[Series[1/((1-x)^2*(1-x^2)*(1-x^5)), {x, 0, 50}], x] (* Vincenzo Librandi, Feb 24 2012 *)
LinearRecurrence[{2, 0, -2, 1, 1, -2, 0, 2, -1}, {1, 2, 4, 6, 9, 13, 18, 24, 31}, 60] (* Harvey P. Dale, Oct 03 2018 *)
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PROG
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(PARI) a(n)=floor((n+8)*(2*n^2+11*n+18)/120) \\ Tani Akinari, May 14 2014
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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