OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Clark Kimberling and John E. Brown, Partial Complements and Transposable Dispersions, J. Integer Seqs., Vol. 7, 2004.
Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).
FORMULA
a(n) = 1 + floor( n(n+1)/6 ). - Michael Somos, Jun 16 1999
a(n) = 1 + A001840(n-1). - Michael Somos, Jun 16 1999
a(n) = 1 + a(n-1) + a(n-3) - a(n-4) if n>4; a(n) = n if n=1..4. - Michael Somos, Jun 16 1999
a(-1-n) = a(n). - Michael Somos, Sep 06 2013
EXAMPLE
G.f. = 1 + x + 2*x^2 + 3*x^3 + 4*x^4 + 6*x^5 + 8*x^6 + 10*x^7 + 13*x^8 + ...
MAPLE
A061347 := proc(n) op(1+(n mod 3), [-2, 1, 1]) ; end proc:
seq(A008748(n), n=0..60) ; # R. J. Mathar, Mar 22 2011
MATHEMATICA
Table[Floor[((n*(n+1)+2)/2+3)/3], {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2010 *)
CoefficientList[Series[(1+x^5)/((1-x)(1-x^2)(1-x^3)), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 11 2013 *)
LinearRecurrence[{2, -1, 1, -2, 1}, {1, 1, 2, 3, 4}, 60] (* Harvey P. Dale, Apr 08 2019 *)
PROG
(PARI) {a(n) = (n^2 + n)\6 + 1} /* Michael Somos, Sep 06 2013 */
(Magma) [1 + Floor(n*(n+1)/6): n in [0..60]]; // G. C. Greubel, Aug 03 2019
(Sage) ((1 + x^5)/((1-x)*(1-x^2)*(1-x^3))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Aug 03 2019
(GAP) List([0..60], n-> 1 + Int(n*(n+1)/6)); # G. C. Greubel, Aug 03 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved