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 A008671 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^7)). 2
 1, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 13, 14, 14, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 28, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 57, 58, 60, 62, 63, 65, 67, 69, 70, 73, 74, 76, 78, 80 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Number of partitions of n into parts 2, 3, and 7. - Joerg Arndt, Jul 08 2013 REFERENCES A. Adler, Hirzebruch's curves F_1, F_2, F_4, F_14, F_28 for Q(sqrt 7), pp. 221-285 of S. Levy, ed., The Eightfold Way, Cambridge Univ. Press, 1999 (see p. 262). L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 24). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 227 Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,-1,0,1,0,-1,-1,0,1). FORMULA Euler transform of length 7 sequence [ 0, 1, 1, 0, 0, 0, 1]. - Michael Somos, Oct 11 2006 a(n) = a(-12-n), a(n) = a(n-2) + a(n-3) - a(n-5) + a(n-7) - a(n-9) - a(n-10) + a(n-12) for all n in Z. - Michael Somos, Oct 11 2006 a(n) = floor((3*n^2+36*n+196)/252 + (-1/9)*(-2)^floor((n+2-3*floor((n+2)/3))/2)). - Tani Akinari, Jul 07 2013 a(n) ~ 1/84*n^2. - Ralf Stephan, Apr 29 2014 0 = a(n) - a(n+2) - a(n+3) + a(n+5) - (mod(n, 7) == 2) for all n in Z. - Michael Somos, Mar 18 2015 a(n) = A008614(2*n). - Michael Somos, Mar 18 2015 EXAMPLE G.f. = 1 + x^2 + x^3 + x^4 + x^5 + 2*x^6 + 2*x^7 + 2*x^8 + 3*x^9 + 3*x^10 + ... MAPLE seq(coeff(series(1/((1-x^2)*(1-x^3)*(1-x^7)), x, n+1), x, n), n = 0..80); # G. C. Greubel, Sep 08 2019 MATHEMATICA CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^7)), {x, 0, 80}], x] (* Vincenzo Librandi, Jun 22 2013 *) a[ n_] := With[{m = If[ n < 0, -12 - n, n]}, SeriesCoefficient[ 1 / ((1 - x^2) (1 - x^3) (1 - x^7)), {x, 0, m}]]; (* Michael Somos, Mar 18 2015 *) a[ n_] := Quotient[ 3 n^2 + 36 n + If[ OddQ[n], 189, 252], 252]; (* Michael Somos, Mar 18 2015 *) PROG (PARI) {a(n) = if( n<0, n = -12-n); polcoeff( 1 / ((1 - x^2) * (1 - x^3) * (1 - x^7)) + x * O(x^n), n)}; /* Michael Somos, Oct 11 2006 */ (PARI) {a(n) = (3*n^2 + 36*n + if( n%2, 189, 252)) \ 252}; /* Michael Somos, Mar 18 2015 */ (MAGMA) R:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x^2)*(1-x^3)*(1-x^7)) )); // G. C. Greubel, Sep 08 2019 (Sage) def A008671_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P(1/((1-x^2)*(1-x^3)*(1-x^7))).list() A008671_list(80) # G. C. Greubel, Sep 08 2019 (GAP) a:=[1, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3];; for n in [13..80] do a[n]:=a[n-2] +a[n-3] -a[n-5] +a[n-7] -a[n-9] -a[n-10] +a[n-12]; od; a; # G. C. Greubel, Sep 08 2019 CROSSREFS First differences of A029001. Cf. A008614. Sequence in context: A226033 A054404 A307152 * A199017 A189709 A025771 Adjacent sequences:  A008668 A008669 A008670 * A008672 A008673 A008674 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified April 10 02:39 EDT 2020. Contains 333392 sequences. (Running on oeis4.)