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A328545
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Number of 11-regular partitions of n (no part is a multiple of 11).
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12
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1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 55, 76, 99, 132, 171, 224, 286, 370, 468, 597, 750, 945, 1177, 1472, 1820, 2255, 2772, 3410, 4165, 5092, 6185, 7515, 9085, 10978, 13207, 15884, 19025, 22774, 27170, 32388, 38489, 45705, 54120, 64030, 75569, 89100
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OFFSET
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0,3
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REFERENCES
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Kathiravan, T., and S. N. Fathima. "On L-regular bipartitions modulo L." The Ramanujan Journal 44.3 (2017): 549-558.
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LINKS
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FORMULA
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a(n) ~ exp(Pi*sqrt(2*n*(s-1)/(3*s))) * (s-1)^(1/4) / (2 * 6^(1/4) * s^(3/4) * n^(3/4)) * (1 + ((s-1)^(3/2)*Pi/(24*sqrt(6*s)) - 3*sqrt(6*s) / (16*Pi * sqrt(s-1))) / sqrt(n) + ((s-1)^3*Pi^2/(6912*s) - 45*s/(256*(s-1)*Pi^2) - 5*(s-1)/128) / n), set s=11. - Vaclav Kotesovec, Aug 01 2022
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MAPLE
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f:=(k, M) -> mul(1-q^(k*j), j=1..M);
LRP := (L, M) -> f(L, M)/f(1, M);
s := L -> seriestolist(series(LRP(L, 80), q, 60));
s(11);
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MATHEMATICA
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Table[Count[IntegerPartitions@n, x_ /; ! MemberQ [Mod[x, 11], 0, 2] ], {n, 0, 46}]
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CROSSREFS
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Number of r-regular partitions for r = 2 through 12: A000009, A000726, A001935, A035959, A219601, A035985, A261775, A104502, A261776, A328545, A328546.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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