A328685 Row sums of A309038.

0, 4, 28, 120, 320, 716, 1380, 2464, 3984, 6196, 9124, 13128, 18048, 24476, 32244, 42096, 53440, 67460, 83604, 103192, 124944, 150892, 179908, 214080, 251184, 294356, 341700, 396264, 454624, 521276, 593364, 675088, 761568, 858916, 963124, 1079736, 1202160, 1338380

Offset: 0

Author

Stefano Spezia, Oct 25 2019

Keywords

• nonn

Comments

All the terms are even.

Links

• Stefano Spezia, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A000583, A309038, A326118, A327479, A327480.

Programs

Mathematica

(* The function T is defined in A309038. *)
Flatten[Table[Sum[T[n, k], {k, 0, n^2}], {n, 0, 37}]]

Formula

Conjectures from Colin Barker, Oct 25 2019: (Start)

G.f.: 4*x*(1 + 5*x + 17*x^2 + 27*x^3 + 46*x^4 + 52*x^5 + 54*x^6 + 28*x^7 + 29*x^8 - 7*x^9+ 5*x^10 - 17*x^11 + 4*x^12 - 6*x^13 + 12*x^14 - 14*x^15 + 8*x^16 - 4*x^17) / ((1 - x)^5*(1 + x)^3*(1 + x^2)^3).

a(n) = 2*a(n-1) - a(n-2) + 3*a(n-4) - 6*a(n-5) + 3*a(n-6) - 3*a(n-8) + 6*a(n-9) - 3*a(n-10) + a(n-12) - 2*a(n-13) + a(n-14) for n > 18.

(End)

a(n) ~ 5*n^4/8. - Conjectured by Stefano Spezia, Sep 08 2021