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 A008748 Expansion of (1 + x^5) / ((1-x) * (1-x^2) * (1-x^3)) in powers of x. 3
 1, 1, 2, 3, 4, 6, 8, 10, 13, 16, 19, 23, 27, 31, 36, 41, 46, 52, 58, 64, 71, 78, 85, 93, 101, 109, 118, 127, 136, 146, 156, 166, 177, 188, 199, 211, 223, 235, 248, 261, 274, 288, 302, 316, 331, 346, 361, 377, 393, 409, 426, 443, 460, 478, 496, 514, 533, 552, 571 (list; graph; refs; listen; history; text; internal format)
 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: A008748 := proc(n) 1/6*n^2+1/6*n+8/9+A061347(n+2)/9 ; 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 Cf. A001840, A008748, A061347. Sequence in context: A025695 A025694 A022796 * A089649 A049700 A002984 Adjacent sequences:  A008745 A008746 A008747 * A008749 A008750 A008751 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified September 18 18:20 EDT 2019. Contains 327178 sequences. (Running on oeis4.)