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A274248 Row sums of A273751.

%I A274248 #24 Oct 20 2023 06:47:47
%S A274248 1,5,16,37,72,124,197,294,419,575,766,995,1266,1582,1947,2364,2837,
%T A274248 3369,3964,4625,5356,6160,7041,8002,9047,10179,11402,12719,14134,
%U A274248 15650,17271,19000,20841,22797,24872,27069,29392,31844,34429,37150,40011,43015,46166
%N A274248 Row sums of A273751.
%H A274248 G. C. Greubel, <a href="/A274248/b274248.txt">Table of n, a(n) for n = 1..1000</a>
%H A274248 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A274248 a(n) = (14*n^3 - 3*n^2 + 10*n + 3*mod(n, 2))/24.
%F A274248 G.f.: x*(1 + 2*x + 3*x^2 + x^3)/((1 - x)^4*(1 + x)). - _Ilya Gutkovskiy_, Jun 17 2016
%F A274248 E.g.f.: (1/48)*( -3*exp(-x) + (3 + 42*x + 78*x^2 + 28*x^3)*exp(x) ). - _G. C. Greubel_, Oct 19 2023
%t A274248 (* First program *)
%t A274248 T[n_, k_]:= T[n, k]= Which[k==n, n(n-1) + 1, k==n-1, (n-1)^2 + 1, k==1, n + T[n-2, 1], 1 < k < n-1, T[n-1, k+1] + 1, True, 0];
%t A274248 a[n_]:= Sum[T[n, k], {k, 1, n}];
%t A274248 Array[a, 40]
%t A274248 (* second program: *)
%t A274248 LinearRecurrence[{3, -2, -2, 3, -1}, {1, 5, 16, 37, 72}, 50] (* _Vincenzo Librandi_, Jun 16 2016 *)
%o A274248 (Magma) [(n*(20-6*n+28*n^2) + 3*(1-(-1)^n))/48: n in [1..40]]; // _G. C. Greubel_, Oct 19 2023
%o A274248 (SageMath) [(n*(20-6*n+28*n^2) + 6*(n%2))/48 for n in range(1,41)] # _G. C. Greubel_, Oct 19 2023
%Y A274248 Cf. A002623, A173196 (same recurrence), A273751.
%K A274248 nonn
%O A274248 1,2
%A A274248 _Jean-François Alcover_ and _Paul Curtz_, Jun 16 2016