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 A123579 The Kruskal-Macaulay function M_3(n). 4
 0, 1, 2, 3, 3, 4, 5, 5, 6, 6, 6, 7, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 23, 23, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 26, 27, 27, 27 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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). REFERENCES D. E. Knuth, The Art of Computer Programming, Vol. 4, Fascicle 3, Section 7.2.1.3, Table 3. LINKS B. M. Abrego, S. Fernandez-Merchant, B. Llano, An Inequality for Macaulay Functions, J. Int. Seq. 14 (2011) # 11.7.4 MAPLE 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: A123579 := proc(n) M(n, 3) ; end: for n from 0 to 120 do printf("%d, ", A123579(n)) ; od ; # R. J. Mathar, Mar 14 2007 CROSSREFS For M_i(n), i=1, 2, 3, 4, 5 see A000127, A123578, A123579, A123580, A123731. Sequence in context: A302779 A296020 A266350 * A166493 A005185 A119466 Adjacent sequences:  A123576 A123577 A123578 * A123580 A123581 A123582 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Nov 12 2006 STATUS approved

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Last modified July 5 05:47 EDT 2022. Contains 355087 sequences. (Running on oeis4.)