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.
KEYWORD
sign,easy
AUTHOR
Alex Ratushnyak, May 09 2012
STATUS
approved