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%I #15 Mar 01 2023 13:11:32
%S 1,7,23,55,109,191,307,463,665,919,1231,1607,2053,2575,3179,3871,4657,
%T 5543,6535,7639,8861,10207,11683,13295,15049,16951,19007,21223,23605,
%U 26159,28891,31807,34913,38215,41719,45431,49357,53503,57875,62479,67321,72407
%N a(n) = (n+1)^3 - n^2.
%H Reinhard Zumkeller, <a href="/A261893/b261893.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = n^3 + 2*n^2 + 3*n + 1.
%F a(n) = A000578(n+1) - A000290(n).
%F O.g.f.: (1 + 3*x + x^2 + x^3)/(1 - x)^4. - _Bruno Berselli_, Jul 04 2016
%F E.g.f.: (1 + 6*x + 5*x^2 + x^3)*exp(x). - _Bruno Berselli_, Jul 04 2016
%t Table[n^3 + 2 n^2 + 3 n + 1, {n, 0, 50}] (* _Bruno Berselli_, Jul 04 2016 *)
%t LinearRecurrence[{4,-6,4,-1},{1,7,23,55},50] (* _Harvey P. Dale_, Mar 01 2023 *)
%o (Haskell)
%o a261893 n = n * (n * (n + 2) + 3) + 1
%o a261893_list = zipWith (-) (tail a000578_list) a000290_list
%o (PARI) vector(50, n, n--; n^3+2*n^2+3*n+1) \\ _Bruno Berselli_, Jul 04 2016
%o (Sage) [n^3+2*n^2+3*n+1 for n in range(50)]; # _Bruno Berselli_, Jul 04 2016
%o (Maxima) makelist(n^3+2*n^2+3*n+1, n, 0, 50); /* _Bruno Berselli_, Jul 04 2016 */
%o (Magma) [n^3+2*n^2+3*n+1: n in [0..50]]; // _Bruno Berselli_, Jul 04 2016
%Y Cf. A000290, A000578.
%Y Subsequence of A167222.
%K nonn,easy
%O 0,2
%A _Reinhard Zumkeller_, Sep 05 2015
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