A274248 Row sums of A273751.

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

Offset: 1

Author

Jean-François Alcover and Paul Curtz, Jun 16 2016

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Crossrefs

Cf. A002623, A173196 (same recurrence), A273751.

Programs

Magma

[(n*(20-6*n+28*n^2) + 3*(1-(-1)^n))/48: n in [1..40]]; // G. C. Greubel, Oct 19 2023

Mathematica

(* 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 *)

SageMath

[(n*(20-6*n+28*n^2) + 6*(n%2))/48 for n in range(1,41)] # G. C. Greubel, Oct 19 2023

Formula

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