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Search: id:A123578
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| A123578 |
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The Kruskal-Macaulay function M_2(n). |
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+0
6
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| 0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Write n (uniquely) as n = C(n_t,t) + C(n_{t-1},t-1) + ... + C(n_v,v) where n_t > n_{t-1} > ... > n_v >= v >= 1. Then M_t(n) = C(n_t-1,t-1) + C(n_{t-1}-1,t-2) + ... + C(n_v-1,v-1).
Apart from the initial 0, this is a duplicate of A002024. - njas, Nov 25 2009
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Vol. 4, Fascicle 3, Section 7.2.1.3, Table 3.
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MAPLE
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lowpol := proc(n, t) local x::integer ; x := floor( (n*factorial(t))^(1/t)) ; while binomial(x, t) <= n do x := x+1 ; od ; RETURN(x-1) ; end: C := proc(n, t) local nresid, tresid, m, a ; nresid := n ; tresid := t ; a := [] ; while nresid > 0 do m := lowpol(nresid, tresid) ; a := [op(a), m] ; nresid := nresid - binomial(m, tresid) ; tresid := tresid-1 ; od ; RETURN(a) ; end: M := proc(n, t) local a ; a := C(n, t) ; add( binomial(op(i, a)-1, t-i), i=1..nops(a)) ; end: A123578 := proc(n) M(n, 2) ; end: for n from 0 to 120 do printf("%d, ", A123578(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leideuniv.nl), Mar 14 2007
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CROSSREFS
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For M_i(n), i=1, 2, 3, 4, 5 see A000127, A123578, A123579, A123580, A123731.
Cf. A002024.
Sequence in context: A087847 A107436 A002024 this_sequence A087845 A130146 A113764
Adjacent sequences: A123575 A123576 A123577 this_sequence A123579 A123580 A123581
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KEYWORD
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nonn,easy,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 12 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leideuniv.nl), Mar 14 2007
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