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 A123574 The Kruskal-Macaulay function K_5(n). 3
 0, 5, 9, 12, 14, 15, 15, 19, 22, 24, 25, 25, 28, 30, 31, 31, 33, 34, 34, 35, 35, 35, 39, 42, 44, 45, 45, 48, 50, 51, 51, 53, 54, 54, 55, 55, 55, 58, 60, 61, 61, 63, 64, 64, 65, 65, 65, 67, 68, 68, 69, 69, 69, 70, 70, 70, 70, 74, 77, 79, 80, 80, 83, 85, 86, 86, 88, 89, 89, 90 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 K_t(n) = C(n_t,t-1) + C(n_{t-1},t-2) + ... + C(n_v,v-1). REFERENCES D. E. Knuth, The Art of Computer Programming, Vol. 4, Fascicle 3, Section 7.2.1.3, Table 3. LINKS 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: K := proc(n, t) local a ; a := C(n, t) ; add( binomial(op(i, a), t-i), i=1..nops(a)) ; end: A123574 := proc(n) K(n, 5) ; end: for n from 0 to 80 do printf("%d, ", A123574(n)) ; od ; # R. J. Mathar, May 18 2007 CROSSREFS For K_i(n), i=1, 2, 3, 4, 5 see A000012, A003057, A123572, A123573, A123574. Sequence in context: A135979 A287452 A287456 * A314611 A143834 A314612 Adjacent sequences:  A123571 A123572 A123573 * A123575 A123576 A123577 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Nov 12 2006 EXTENSIONS More terms from R. J. Mathar, May 18 2007 STATUS approved

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Last modified October 1 04:06 EDT 2020. Contains 337441 sequences. (Running on oeis4.)