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A077229
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Number of compositions of n where the largest part is less than or equal to the number of parts.
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7
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1, 1, 3, 5, 11, 23, 48, 98, 204, 421, 863, 1766, 3606, 7341, 14913, 30233, 61175, 123589, 249344, 502443, 1011366, 2033894, 4086975, 8206833, 16469875, 33035611, 66234372, 132745859, 265961487, 532717894, 1066778687, 2135822457
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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LINKS
| Index entries for sequences related to compositions
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FORMULA
| G.f.: Sum(((x^(k+1)-x)/(x-1))^k, k=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 24 2004
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EXAMPLE
| a(5)=11 since 5 can be written as 1+1+1+1+1, 1+1+1+2, 1+1+2+1, 1+1+3, 1+2+1+1, 1+2+2, 1+3+1, 2+1+1+1, 2+1+2, 2+2+1, or 3+1+1; but not as 2+3 since then the largest part (3) would be greater than the number of parts (2).
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CROSSREFS
| Row sums of A077227.
Cf. A064174.
Sequence in context: A032803 A030494 A084361 * A018113 A113281 A037446
Adjacent sequences: A077226 A077227 A077228 * A077230 A077231 A077232
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Oct 29 2002
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 24 2004
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