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Search: id:A100853
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| A100853 |
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Number of partitions of n in which every part occurs 1, 4, or 5 times. Also number of partitions of n in which every part is congruent to {1, 3, 4, 5, 7} mod 8. |
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1
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| 1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 15, 19, 25, 31, 38, 48, 59, 72, 88, 107, 130, 157, 188, 225, 270, 321, 380, 451, 533, 627, 737, 864, 1011, 1181, 1375, 1599, 1858, 2152, 2488, 2875, 3316, 3816, 4387, 5036, 5773, 6610, 7555, 8626, 9840, 11207, 12748, 14489
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Also number of partitions of n in which every even part occurs exactly twice. - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 06 2007
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FORMULA
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Euler transform of period 8 sequence [1, 0, 1, 1, 1, 0, 1, 0, ...]. G.f.: Product_{k>0} (1+x^k)*(1+x^(4*k)) = 1/Product_{k>0} (1-x^A047501(k)).
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MAPLE
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seq(coeff(mul((1+x^k)*(1+x^(4*k)), k=1..100), x, n), n=0..60); (C. Ronaldo)
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CROSSREFS
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Cf. A089958.
Sequence in context: A062188 A122129 A003413 this_sequence A121659 A096814 A039861
Adjacent sequences: A100850 A100851 A100852 this_sequence A100854 A100855 A100856
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 08 2005
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EXTENSIONS
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More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 19 2005
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