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Search: id:A123573
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| A123573 |
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The Kruskal-Macaulay function K_4(n). |
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+0
3
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| 0, 4, 7, 9, 10, 10, 13, 15, 16, 16, 18, 19, 19, 20, 20, 20, 23, 25, 26, 26, 28, 29, 29, 30, 30, 30, 32, 33, 33, 34, 34, 34, 35, 35, 35, 35, 38, 40, 41, 41, 43, 44, 44, 45, 45, 45, 47, 48, 48, 49, 49, 49, 50, 50, 50, 50, 52, 53, 53, 54, 54, 54, 55, 55, 55, 55, 56, 56, 56, 56, 56
(list; graph; listen)
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OFFSET
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0,2
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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 K_t(n) = C(n_t,t-1) + C(n_{t-1},t-2) + ... + C(n_v,v-1).
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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: K := proc(n, t) local a ; a := C(n, t) ; add( binomial(op(i, a), t-i), i=1..nops(a)) ; end: A123573 := proc(n) K(n, 4) ; end: for n from 0 to 80 do printf("%d, ", A123573(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 18 2007
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CROSSREFS
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For K_i(n), i=1, 2, 3, 4, 5 see A000012, A003057, A123572, A123573, A123574.
Sequence in context: A085108 A106502 A046254 this_sequence A085746 A081828 A153053
Adjacent sequences: A123570 A123571 A123572 this_sequence A123574 A123575 A123576
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KEYWORD
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nonn,easy
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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.leidenuniv.nl), May 18 2007
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