A152895 -id:A152895 - cp's OEIS frontend

A152896 a=b=c=0;c(n)=c+n+a;b(n)=b+n+c;a(n)=a+n+b.

0, 3, 15, 55, 183, 588, 1865, 5887, 18550, 58414, 183904, 578936, 1822459, 5736946, 18059358, 56849069, 178955165, 563332829, 1773314909, 5582216334, 17572253459, 55315679765, 174128175040, 548137914348, 1725482812062

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 14 2008

nonn

Index entries for linear recurrences with constant coefficients, signature (6, -12, 11, -5, 1).

Cf. A152891, A152895

lst={};a=b=c=0;Do[c+=n+a;b+=n+c;a+=n+b;AppendTo[lst,a],{n,0,2*4!}];lst
LinearRecurrence[{6,-12,11,-5,1},{0,3,15,55,183},30] (* Harvey P. Dale, Dec 11 2014 *)

G.f.: x^2(3-3x+x^2)/((1-x)^2*(1-4x+3x^2-x^3)). a(n)=6*a(n-1)-12*a(n-2)+11*a(n-3)-5*a(n-4)+a(n-5). [From R. J. Mathar, Dec 15 2008]

A152897 Partial sums of A152896.

Original entry on oeis.org

0, 3, 18, 73, 256, 844, 2709, 8596, 27146, 85560, 269464, 848400, 2670859, 8407805, 26467163, 83316232, 262271397, 825604226, 2598919135, 8181135469, 25753388928, 81069068693, 255197243733, 803335158081, 2528817970143

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 14 2008

nonn

Index entries for linear recurrences with constant coefficients, signature (7,-18,23,-16,6,-1).

Cf. A152891, A152895, A152896.

lst={};a=b=c=s=0;Do[c+=n+a;b+=n+c;a+=n+b;s+=a;AppendTo[lst,s],{n,0,2*4!}];lst
Rest[CoefficientList[Series[x^2(3-3x+x^2)/((1-x)^3(1-4x+3x^2-x^3)),{x,0,40}],x]]  (* Harvey P. Dale, Mar 11 2011 *)
LinearRecurrence[{7,-18,23,-16,6,-1},{0,3,18,73,256,844},30] (* Harvey P. Dale, Feb 07 2015 *)

a(n)=A124820(n)-A000217(n+1). G.f.: x^2(3-3x+x^2)/((1-x)^3*(1-4x+3x^2-x^3)). [From R. J. Mathar, Dec 15 2008]

a(1)=0, a(2)=3, a(3)=18, a(4)=73, a(5)=256, a(6)=844, a(n)=7*a(n-1)- 18*a(n-2)+ 23*a(n-3)-16*a(n-4)+6*a(n-5)-a (n-6). - Harvey P. Dale, Feb 07 2015

cp's OEIS Frontend

A152896 a=b=c=0;c(n)=c+n+a;b(n)=b+n+c;a(n)=a+n+b.

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