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

Author

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

Keywords

• sign

Comments

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

Examples

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

Links

• 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).

Crossrefs

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

Programs

Maple

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

Mathematica

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

PARI

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

Formula

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

Extensions

More terms from Emeric Deutsch, Oct 23 2006