A236294 a(n) = max( a(n-1) + a(n-3), 2*a(n-2) ) - a(n-4), with a(0)=1, a(1)=1, a(2)=2, a(3)=3.

1, 1, 2, 3, 3, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 22, 25, 27, 30, 33, 35, 39, 42, 45, 49, 52, 56, 60, 63, 68, 72, 76, 81, 85, 90, 95, 99, 105, 110, 115, 121, 126, 132, 138, 143, 150, 156, 162, 169, 175, 182, 189, 195, 203, 210, 217, 225, 232, 240, 248, 255

Offset: 0

Author

Michael Somos, Jan 21 2014

Keywords

• nonn
• easy

Comments

Tropical version of Somos-4 sequence A006720.

Second difference is period 8 sequence [1, 0, -1, 2, -1, 0, 1, -1, ...]

The numerator of the g.f. is the reciprocal polynomial of the numerator of the g.f. of A220838.

Examples

			G.f. = 1 + x + 2*x^2 + 3*x^3 + 3*x^4 + 5*x^5 + 6*x^6 + 7*x^7 + 9*x^8 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,1,-2,1).

Crossrefs

Cf. A006720, A220838.

Programs

Magma

m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x+x^2-x^4+2*x^5-x^6)/((1-x)^2*(1-x^8)))); // G. C. Greubel, Aug 07 2018

Mathematica

CoefficientList[Series[(1-x+x^2-x^4+2*x^5-x^6)/((1-x)^2*(1-x^8)), {x, 0, 50}], x] (* G. C. Greubel, Aug 07 2018 *)

PARI

{a(n) = if( n<-4, n = -8-n); if( n<0, -(n==-4), polcoeff( (1 - x + x^2 - x^4 + 2*x^5 - x^6) / ( (1 - x)^2 * (1 - x^8) ) + x * O(x^n), n))};

Formula

G.f.: (1 - x + x^2 - x^4 + 2*x^5 - x^6) / ( (1 - x)^2 * (1 - x^8) ).

a(n) = a(-8 - n) = A220838(n + 5) for all n in Z.

0 = (a(n+5) - 2*a(n+3) + a(n+1)) * (a(n+4) - 2*a(n+2) * a(n)) for all n in Z.