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

1,2

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).

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

a(n) ~ 7*n^3/12. - Charles R Greathouse IV, May 31 2026

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 *)

Prog

(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
(PARI) a(n)=n*(20-6*n+28*n^2)\/48 \\ Charles R Greathouse IV, May 31 2026

Crossrefs

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

Sequence in context: A264552 A128848 A390565 * A188427 A022496 A372403

Adjacent sequences: A274245 A274246 A274247 * A274249 A274250 A274251

Keyword

nonn,easy,changed

Author

Jean-François Alcover and Paul Curtz, Jun 16 2016

Status

approved