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%I #39 Mar 08 2023 12:03:24
%S 2,11,29,56,92,137,191,254,326,407,497,596,704,821,947,1082,1226,1379,
%T 1541,1712,1892,2081,2279,2486,2702,2927,3161,3404,3656,3917,4187,
%U 4466,4754,5051,5357,5672,5996,6329,6671,7022,7382,7751,8129,8516,8912,9317
%N a(n) = (9n^2 + 9n + 4)/2.
%C Third column of A046741.
%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(2.3.14).
%H Harry J. Smith, <a href="/A062123/b062123.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: (1+2*x)*(2+x)/(1-x)^3. Generally, g.f. for k-th column of A046741 is coefficient of y^k in expansion of (1-y)/((1-y-y^2)*(1-y)-(1+y)*x).
%F a(n) = 9*n + a(n-1), with n>0, a(0)=2. - _Vincenzo Librandi_, Aug 07 2010
%F E.g.f.: (4 +18*x +9*x^2)*exp(x)/2. - _G. C. Greubel_, Jan 31 2019
%t Table[2 +9*n*(1+n)/2, {n,0,50}] (* _G. C. Greubel_, Jan 31 2019 *)
%t LinearRecurrence[{3,-3,1},{2,11,29},50] (* _Harvey P. Dale_, Jan 12 2020 *)
%o (PARI) for (n=0, 1000, write("b062123.txt", n, " ", 2 + (n + n^2)*9/2) ) \\ _Harry J. Smith_, Aug 02 2009
%o (Magma) [2 +9*n*(1+n)/2: n in [0..50]]; // _G. C. Greubel_, Jan 31 2019
%o (Sage) [2 +9*n*(1+n)/2 for n in range(50)] # _G. C. Greubel_, Jan 31 2019
%o (GAP) List([0..50], n -> 2 +9*n*(1+n)/2); # _G. C. Greubel_, Jan 31 2019
%Y Cf. dumbbells: A002940, A002941, A002889, A046741, A055608, A062124-A062127.
%Y Cf. A235332.
%K nonn,easy
%O 0,1
%A _Vladeta Jovovic_, Jun 04 2001
%E More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001
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