cp's OEIS Frontend

A228219 Number of second differences of arrays of length 4 of numbers in 0..n.

%I A228219 #12 Mar 16 2018 10:01:30
%S A228219 15,49,103,177,271,385,519,673,847,1041,1255,1489,1743,2017,2311,2625,
%T A228219 2959,3313,3687,4081,4495,4929,5383,5857,6351,6865,7399,7953,8527,
%U A228219 9121,9735,10369,11023,11697,12391,13105,13839,14593,15367,16161,16975,17809
%N A228219 Number of second differences of arrays of length 4 of numbers in 0..n.
%C A228219 Row 2 of A228218.
%H A228219 R. H. Hardin, <a href="/A228219/b228219.txt">Table of n, a(n) for n = 1..210</a>
%F A228219 Empirical: a(n) = 10*n^2 + 4*n + 1 = A272039(n).
%F A228219 Conjectures from _Colin Barker_, Mar 16 2018: (Start)
%F A228219 G.f.: x*(15 + 4*x + x^2) / (1 - x)^3.
%F A228219 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F A228219 (End)
%e A228219 Some solutions for n=4:
%e A228219 ..1....1....1....5....6....1....2...-5....8....4...-5....8....1....5...-7....0
%e A228219 ..4....2...-3....1...-6....1....1...-1...-7....1....0...-4....5...-7....6....6
%Y A228219 Cf. A228218, A272039.
%K A228219 nonn
%O A228219 1,1
%A A228219 _R. H. Hardin_, Aug 16 2013