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A034296
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Number of flat partitions of n: partitions {a_i} with each |a_i-a_{i-1}| <= 1.
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12
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1, 2, 3, 4, 5, 7, 8, 10, 13, 15, 18, 23, 26, 31, 39, 44, 52, 63, 72, 85, 101, 115, 134, 158, 181, 208, 243, 277, 318, 369, 418, 478, 549, 622, 710, 809, 914, 1036, 1177, 1328, 1498, 1695, 1904, 2143, 2416, 2706, 3036, 3408, 3811, 4264
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also number of partitions of n such that all parts, with the possible exception of the largest, appear only once. Example: a(6)=7 because we have [6],[5,1],[4,2],[3,3],[3,2,1],[2,2,2] and [1,1,1,1,1,1] ([4,1,1],[3,1,1,1],[2,2,1,1],[2,1,1,1,1,1] do not qualify). - Emeric Deutsch (deutsch(AT)duke.poly.edu) and Vladeta Jovovic, Feb 23 2006
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FORMULA
| G.f.: x/(1-x)+x^2/(1-x^2)*(1+x)+x^3/(1-x^3)*(1+x)*(1+x^2)+x^4/(1-x^4)*(1+x)*(1+x^2)*(1+x^3)+x^5/(1-x^5)*(1+x)*(1+x^2)*(1+x^3)*(1+x^4)+... . - Emeric Deutsch and Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 22 2006
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MAPLE
| g:=sum(x^j*product(1+x^i, i=1..j-1)/(1-x^j), j=1..60): gser:=series(g, x=0, 55): seq(coeff(gser, x^n), n=1..50); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 23 2006
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CROSSREFS
| Cf. A034297.
Sequence in context: A026496 A008752 A029003 * A075745 A100289 A054021
Adjacent sequences: A034293 A034294 A034295 * A034297 A034298 A034299
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KEYWORD
| nonn
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AUTHOR
| Erich Friedman (erich.friedman(AT)stetson.edu)
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 23 2006
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