This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A008671 #45 Jun 25 2025 09:59:48
%S A008671 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,
%T A008671 16,16,17,18,19,20,21,22,23,24,25,26,28,28,30,31,32,33,35,36,37,39,40,
%U A008671 41,43,44,46,47,49,50,52,53,55,57,58,60,62,63,65,67,69,70,73,74,76,78,80
%N A008671 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^7)).
%C A008671 Number of partitions of n into parts 2, 3, and 7. - _Joerg Arndt_, Jul 08 2013
%D A008671 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).
%D A008671 L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 24).
%H A008671 Vincenzo Librandi, <a href="/A008671/b008671.txt">Table of n, a(n) for n = 0..1000</a>
%H A008671 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=227">Encyclopedia of Combinatorial Structures 227</a>
%H A008671 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,-1,0,1,0,-1,-1,0,1).
%F A008671 Euler transform of length 7 sequence [ 0, 1, 1, 0, 0, 0, 1]. - _Michael Somos_, Oct 11 2006
%F A008671 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
%F A008671 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
%F A008671 a(n) ~ 1/84*n^2. - _Ralf Stephan_, Apr 29 2014
%F A008671 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
%F A008671 a(n) = A008614(2*n). - _Michael Somos_, Mar 18 2015
%F A008671 a(n) = floor((n^2 + 12*n + 56 + 28*[(n mod 3)=0])/84). - _Hoang Xuan Thanh_, Jun 24 2025
%e A008671 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 + ...
%p A008671 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
%t A008671 CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^7)), {x,0,80}], x] (* _Vincenzo Librandi_, Jun 22 2013 *)
%t A008671 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 *)
%t A008671 a[ n_] := Quotient[ 3 n^2 + 36 n + If[ OddQ[n], 189, 252], 252]; (* _Michael Somos_, Mar 18 2015 *)
%t A008671 LinearRecurrence[{0,1,1,0,-1,0,1,0,-1,-1,0,1},{1,0,1,1,1,1,2,2,2,3,3,3},100] (* _Harvey P. Dale_, Dec 18 2023 *)
%o A008671 (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 */
%o A008671 (PARI) {a(n) = (3*n^2 + 36*n + if( n%2, 189, 252)) \ 252}; /* _Michael Somos_, Mar 18 2015 */
%o A008671 (Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x^2)*(1-x^3)*(1-x^7)) )); // _G. C. Greubel_, Sep 08 2019
%o A008671 (Sage)
%o A008671 def A008671_list(prec):
%o A008671 P.<x> = PowerSeriesRing(ZZ, prec)
%o A008671 return P(1/((1-x^2)*(1-x^3)*(1-x^7))).list()
%o A008671 A008671_list(80) # _G. C. Greubel_, Sep 08 2019
%o A008671 (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
%Y A008671 First differences of A029001.
%Y A008671 Cf. A008614.
%K A008671 nonn,easy
%O A008671 0,7
%A A008671 _N. J. A. Sloane_