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 A184825 a(n) = n + floor(n*t) + floor(n*t^2) + floor(n/t), where t is the tetranacci constant. 4
 5, 13, 20, 27, 34, 42, 49, 56, 63, 71, 77, 85, 92, 99, 105, 113, 120, 127, 134, 142, 149, 156, 163, 171, 177, 185, 193, 199, 206, 213, 221, 227, 235, 242, 250, 256, 264, 271, 278, 285, 293, 299, 306, 313, 321, 327, 335, 342, 350, 356, 364, 371, 378, 386, 393, 400, 406, 414, 421, 428, 435, 443, 450, 457, 464, 472, 478, 486, 493, 500, 506, 514, 521, 528, 535, 543, 550, 557, 564, 572, 579, 586, 593, 600, 607, 614, 622, 628, 636, 643, 651, 657, 665, 672, 679, 686, 693, 700, 707, 714, 722, 728, 736, 743, 751, 757 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is one of four sequences that partition the positive integers. Given t is the tetranacci constant, then the following sequences are disjoint: . A184823(n) = n + [n/t] + [n/t^2] + [n/t^3], . A184824(n) = n + [n*t] + [n/t] + [n/t^2], . A184825(n) = n + [n*t] + [n*t^2] + [n/t], . A184826(n) = n + [n*t] + [n*t^2] + [n*t^3], where []=floor. This is a special case of Clark Kimberling's results given in A184812. LINKS Table of n, a(n) for n=1..106. FORMULA Lim_{n->infinity} a(n)/n = t^3 = 7.1618472084864470579236869... a(n) = n + floor(n*p/q) + floor(n*r/q) + floor(n*s/q), where p=t, q=t^2, r=t^3, s=t^4, and t is the tetranacci constant. EXAMPLE Let t be the tetranacci constant, then t^3 = 1 + t + t^2 + 1/t and: t = 1.92756197548..., t^2 = 3.71549516932..., t^3 = 7.16184720848..., t^4 = 13.8049043532... MATHEMATICA With[{t=x/.Last[Solve[x^4==Total[x^Range[0, 3]], x]]}, Table[n+Floor[n t]+Floor[n t^2]+Floor[n/t], {n, 120}]] (* Harvey P. Dale, Feb 02 2011 *) PROG (PARI) {a(n)=local(t=real(polroots(1+x+x^2+x^3-x^4)[2])); n+floor(n*t)+floor(n*t^2)+floor(n/t)} CROSSREFS Cf. A184823, A184824, A184826; A184812, A086088. Sequence in context: A087714 A055045 A213741 * A190372 A184837 A197120 Adjacent sequences: A184822 A184823 A184824 * A184826 A184827 A184828 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 23 2011 STATUS approved

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Last modified August 12 12:28 EDT 2024. Contains 375092 sequences. (Running on oeis4.)