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1, 5, 16, 37, 72, 124, 197, 294, 419, 575, 766, 995, 1266, 1582, 1947, 2364, 2837, 3369, 3964, 4625, 5356, 6160, 7041, 8002, 9047, 10179, 11402, 12719, 14134, 15650, 17271, 19000, 20841, 22797, 24872, 27069, 29392, 31844, 34429, 37150, 40011, 43015, 46166
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (14*n^3 - 3*n^2 + 10*n + 3*mod(n, 2))/24.
G.f.: x*(1 + 2*x + 3*x^2 + x^3)/((1 - x)^4*(1 + x)). - Ilya Gutkovskiy, Jun 17 2016
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
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MATHEMATICA
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(* First program *)
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];
a[n_]:= Sum[T[n, k], {k, 1, n}];
Array[a, 40]
(* second program: *)
LinearRecurrence[{3, -2, -2, 3, -1}, {1, 5, 16, 37, 72}, 50] (* Vincenzo Librandi, Jun 16 2016 *)
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PROG
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(Magma) [(n*(20-6*n+28*n^2) + 3*(1-(-1)^n))/48: n in [1..40]]; // G. C. Greubel, Oct 19 2023
(SageMath) [(n*(20-6*n+28*n^2) + 6*(n%2))/48 for n in range(1, 41)] # G. C. Greubel, Oct 19 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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