A210673 a(n) = a(n-1)+a(n-2)+n-4, a(0)=0, a(1)=1.

0, 1, -1, -1, -2, -2, -2, -1, 1, 5, 12, 24, 44, 77, 131, 219, 362, 594, 970, 1579, 2565, 4161, 6744, 10924, 17688, 28633, 46343, 74999, 121366, 196390, 317782, 514199, 832009, 1346237, 2178276, 3524544, 5702852, 9227429, 14930315, 24157779, 39088130, 63245946

Offset

0,5

Comments

Second differences are Fibonacci numbers A000045 with offset -4. - Olivier Gérard, Aug 21 2016

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).

Formula

a(0)=0, a(1)=1, a(2)=-1, a(3)=-1, a(n) = 3*a(n-1)-2*a(n-2)-a(n-3)+a(n-4). - Harvey P. Dale, Oct 03 2012

G.f.: x/Q(0), where Q(k)= 1 + (k+1)*x/(1 - x - x*(1-x)/(x + (k+1)*(1-x)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Apr 24 2013

G.f.: -x*(2*x-1)^2 / ((x-1)^2*(x^2+x-1)). - Colin Barker, May 31 2013

Mathematica

RecurrenceTable[{a[0]==0, a[1]==1, a[n]==a[n-1]+a[n-2]+n-4}, a, {n, 50}] (* or *) LinearRecurrence[{3, -2, -1, 1}, {0, 1, -1, -1}, 50] (* Harvey P. Dale, Oct 03 2012 *)

Crossrefs

Cf. A066982: a(n)=a(n-1)+a(n-2)+n-2, a(0)=0, a(1)=1 (except the first term).

Cf. A104161: a(n)=a(n-1)+a(n-2)+n-1, a(0)=0, a(1)=1.

Cf. A001924: a(n)=a(n-1)+a(n-2)+n, a(0)=0, a(1)=1.

Cf. A192760: a(n)=a(n-1)+a(n-2)+n+1, a(0)=0, a(1)=1.

Cf. A192761: a(n)=a(n-1)+a(n-2)+n+2, a(0)=0, a(1)=1.

Cf. A192762: a(n)=a(n-1)+a(n-2)+n+3, a(0)=0, a(1)=1.

Cf. A210675: a(n)=a(n-1)+a(n-2)+n+4, a(0)=0, a(1)=1.

Sequence in context: A199803 A304197 A348768 * A129320 A359556 A320844

Adjacent sequences: A210670 A210671 A210672 * A210674 A210675 A210676

Keyword

sign,easy

Author

Alex Ratushnyak, May 09 2012

Status

approved