A125577 -id:A125577 - cp's OEIS frontend

A153026 a(1)=0, a(n) = n^3 - a(n-1).

0, 8, 19, 45, 80, 136, 207, 305, 424, 576, 755, 973, 1224, 1520, 1855, 2241, 2672, 3160, 3699, 4301, 4960, 5688, 6479, 7345, 8280, 9296, 10387, 11565, 12824, 14176, 15615, 17153, 18784, 20520, 22355, 24301, 26352, 28520, 30799, 33201, 35720, 38368

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 17 2008

The old name was: a(n)+a(n+1) = cube: 0+8=8=2^3; 8+19=27=3^3; 19+45=64=4^3; ...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A125577, A153026.

[n le 1 select n-1 else n^3-Self(n-1): n in [1..50]]; // Vincenzo Librandi, May 19 2014

a=1;lst={};Do[a=n^3-a;AppendTo[lst,a],{n,1,5!}];lst
CoefficientList[Series[x (8 - 5 x + 4 x^2 - x^3)/((1 + x) (1 - x)^4), {x, 0, 50}], x] (* Vincenzo Librandi, May 19 2014 *)

From R. J. Mathar, Dec 19 2008: (Start)
G.f.: x^2*(8-5*x+4*x^2-x^3)/((1+x)*(1-x)^4).
a(n)+a(n+1) = A000578(n+1).
a(n)= -1/8+3*n^2/4+n^3/2+9*(-1)^n/8. (End)

Name improved by Alex Ratushnyak, Aug 05 2012

A215097 a(n) = n^3 - a(n-2) for n >= 2 and a(0)=0, a(1)=1.

Original entry on oeis.org

0, 1, 8, 26, 56, 99, 160, 244, 352, 485, 648, 846, 1080, 1351, 1664, 2024, 2432, 2889, 3400, 3970, 4600, 5291, 6048, 6876, 7776, 8749, 9800, 10934, 12152, 13455, 14848, 16336, 17920, 19601, 21384, 23274, 25272, 27379, 29600, 31940, 34400, 36981, 39688, 42526

Offset: 0

Alex Ratushnyak, Aug 03 2012

Index entries for linear recurrences with constant coefficients, signature (4,-7,8,-7,4,-1).

Cf. A000217 (n^2 - a(n-1)).
Cf. A125577 (n^2 - a(n-1) with a(0)=1).
Cf. A011934 (n^3 - a(n-1)).
Cf. A153026 (n^3 - a(n-1) with a(1)=0).
Cf. A194274 (n^2 - a(n-2)).
Cf. A187093 (n^2 - a(n-2) with a(0)=a(1)=1, a(-1)=0).
Cf. A107386 ((n-2)^2 - a(n-1) with a(0)=0, a(1)=a(2)=1, a(3)=2).
Cf. A206481 ((n-1)^3 - a(n-2)).

RecurrenceTable[{a[0] == 0, a[1] == 1, a[n] == n^3 - a[n - 2]}, a[n], {n, 0, 43}] (* Bruno Berselli, Aug 07 2012 *)

prpr = 0
prev = 1
for n in range(2,77):
    print(prpr, end=',')
    curr = n*n*n - prpr
    prpr = prev
    prev = curr

G.f.: (x+4*x^2+x^3)/((-1+x)^4*(1+x^2)). - David Scambler, Aug 06 2012

a(n) = (n*(n^2-3)-(1-(-1)^n)*i^(n+1))/2, where i=sqrt(-1). - Bruno Berselli, Aug 07 2012

cp's OEIS Frontend

A153026 a(1)=0, a(n) = n^3 - a(n-1).

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