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%I #36 Sep 08 2022 08:44:46
%S 0,5,21,48,86,135,195,266,348,441,545,660,786,923,1071,1230,1400,1581,
%T 1773,1976,2190,2415,2651,2898,3156,3425,3705,3996,4298,4611,4935,
%U 5270,5616,5973,6341,6720,7110,7511,7923,8346,8780,9225,9681,10148,10626,11115
%N a(n) = n*(11*n - 1)/2.
%C Number of sets with two elements that can be obtained by selecting distinct elements from two sets with 2n and 3n elements respectively and n common elements. - Polina S. Dolmatova (polinasport(AT)mail.ru), Jul 11 2003
%H G. C. Greubel, <a href="/A022268/b022268.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: x*(5 + 6*x)/(1-x)^3. - _Bruno Berselli_, Feb 11 2011
%F a(n) = 11*n + a(n-1) - 6 for n>0. - _Vincenzo Librandi_, Aug 04 2010
%F a(n) = A000217(6*n-1) - A000217(5*n-1). - _Bruno Berselli_, Oct 17 2016
%F From _Wesley Ivan Hurt_, Dec 04 2016: (Start)
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
%F a(n) = (1/9) * Sum_{i=n..10n-1} i. (End)
%F E.g.f.: (1/2)*(11*x^2 + 10*x)*exp(x). - _G. C. Greubel_, Jul 17 2017
%p A022268:=n->n*(11*n - 1)/2: seq(A022268(n), n=0..50); # _Wesley Ivan Hurt_, Dec 04 2016
%t Table[n (11 n - 1)/2, {n, 0, 40}] (* _Bruno Berselli_, Oct 14 2016 *)
%o (PARI) a(n)=n*(11*n-1)/2 \\ _Charles R Greathouse IV_, Sep 24 2015
%o (Magma) [n*(11*n - 1)/2 : n in [0..50]]; // _Wesley Ivan Hurt_, Dec 04 2016
%Y Cf. A000217, A022281.
%Y Cf. index to sequence with numbers of the form n*(d*n+10-d)/2 in A140090.
%Y Cf. similar sequences listed in A022288.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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