A104101 -id:A104101 - cp's OEIS frontend

A122115 a(n) = a(n-1) + a(n-3) + a(n-5).

-3, -1, 4, 8, 15, 16, 23, 42, 66, 104, 162, 251, 397, 625, 980, 1539, 2415, 3792, 5956, 9351, 14682, 23053, 36196, 56834, 89238, 140116, 220003, 345437, 542387, 851628, 1337181, 2099571, 3296636, 5176204, 8127403, 12761220, 20036995, 31461034, 49398458, 77562856, 121785110, 191220563, 300244453

Offset: 1

Jian Tang (jian.tang(AT)gmail.com), Oct 19 2006

sign

The ratio of successive terms of this sequence converges to the real root of x^5 - x^4 - x^2 - 1 which is approximately 1.5701473... (see A293506). - Iain Fox, Oct 12 2017

			  -3 +  4 + 15 = 16
  -1 +  8 + 16 = 23
   4 + 15 + 23 = 42

Robert Israel, Table of n, a(n) for n = 1..5098
Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, 0, 1).

This sequence includes the "Lost" numbers, 4 8 15 16 23 42, A104101. - Rick Powers (powersr(AT)westerntc.edu), Sep 18 2009

a[1]:=-3: a[2]:=-1: a[3]:=4: a[4]:=8: a[5]:=15: for n from 6 to 45 do a[n]:=a[n-1]+a[n-3]+a[n-5] od: seq(a[n],n=1..45); # Emeric Deutsch, Oct 23 2006

LinearRecurrence[{1,0,1,0,1},{-3,-1,4,8,15},50] (* Harvey P. Dale, Apr 22 2013 *)

first(n) = my(res = vector(n)); res[1] = -3; res[2] = -1; res[3] = 4; res[4] = 8; res[5] = 15; for(i = 6, n, res[i] = res[i-1] + res[i-3] + res[i-5]); res \\ Iain Fox, Oct 23 2017

G.f.: x*(-3 + 2*x + 5x^2 + 7*x^3 + 8*x^4)/(1 - x - x^3 - x^5). - Philippe Deléham, Oct 20 2006

More terms from Emeric Deutsch, Oct 23 2006

A130826 a(n) is the smallest number such that twice the number of divisors of (a(n)-n)/3 gives the n-th term in the first differences of the sequence produced by the Flavius Josephus sieve, A000960.

Original entry on oeis.org

4, 8, 15, 16, 23, 42, 55, 200, 81, 46, 119, 192, 205, 196622, 12303, 88, 449, 558, 127, 1748, 786453, 58, 2183, 3096, 1105, 786458, 12582939, 568, 2189, 2730, 9247, 572, 8673, 3106, 2195, 8676, 145, 110630, 3819, 2200, 786473, 20202, 79, 7604, 7077933

Offset: 1

Stephen Casey (hexomino(AT)gmail.com), Jul 17 2007

The first six terms in the sequence are those from the TV show Lost, see A104101.

			a(8)=200 because the 8th term in A056526 is 14. Half of that is 7. The smallest number with seven divisors is 64 and 64*3 + 8 = 200.

M. E. Andersson, Das Flaviussche Sieb, Acta Arith., 85 (1998), 301-307.
V. Gardiner, R. Lazarus, N. Metropolis and S. Ulam, On certain sequences of integers defined by sieves, Math. Mag., 29 (1955), 117-119.
Index entries for sequences related to the Josephus Problem

Cf. A000960, A056526, A104101, A005179.

Corrected and extended by Alois P. Heinz, Nov 27 2009

cp's OEIS Frontend

A122115 a(n) = a(n-1) + a(n-3) + a(n-5).

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