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Search: id:A035796
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| A035796 |
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Words over signatures (derived from multisets and multinomials). |
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+0
2
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| 1, 2, 2, 3, 18, 4, 48, 6, 5, 36, 100, 144, 6, 200, 180, 600, 7, 450, 900, 294, 24, 300, 1800, 8, 882, 7200, 448, 1200, 1470, 4410, 9, 1568, 22050, 648, 7200, 3136, 1800, 9408, 10, 14700, 2592, 16200, 1960, 56448, 900, 29400, 6048, 22050, 18144
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A reordering of A049009(n)=A049009(p(n)): distribution of words by numeric partition where the partition sequence: p(n)=[1],[2],[1,1],[3],[2,1],[1,1,1],[4],[3,1],[2,2],[2,1,1],... (A036036) is encoded by prime factorization ([P1,P2,P3,...] with P1>=P2>=P3>=... is encoded as 2^P1 * 3^P2 * 5^P3 *...): ep(n)=2,4,6,8,12,30,16,24,36,60, ... (A063008(n)) and then sorted: s(m)=2,4,6,8,12,16,24,30,32,36,48,60,... (025487(m+1)). Hence A035796(n)=A049009(s(m)).
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 831.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
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FORMULA
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a(n)=A049009(p) where p is such that A063008(p)=A025487(n+1).
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EXAMPLE
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27 = a(4) + a(5) + a(8) since a8(4) = 3, a12(5) = 18, a30(8) = 6; 256 = a(6) + a(7) + a(10) + a(12) + a(21) = 4 + 48 + 36 + 144 + 24
27 = a(4) + a(5) + a(8) = A049009(4) + A049009(5) + A049009(6) = 3 + 18 + 6 since A063008(4) = 8 =A025487(4+1), A063008(5)= 12 =A025487(5+1), A063008(6)= 30 =A025487(8+1);...
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CROSSREFS
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Cf. A000312, A025487, A019575, A001700, A005651, A036036, A063008, A025487, A049009.
Adjacent sequences: A035793 A035794 A035795 this_sequence A035797 A035798 A035799
Sequence in context: A109843 A089751 A137909 this_sequence A049009 A101817 A058159
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KEYWORD
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nonn
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AUTHOR
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Alford Arnold (Alford1940(AT)aol.com)
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EXTENSIONS
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More terms and additional comments from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 02 2001
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