A354608 - OEIS

%I #15 Jul 08 2022 16:11:54

%S 0,1,44,541,3236,12885,39656,102249,231736,476121,905620,1618661,

%T 2748604,4471181,7012656,10658705,15764016,22762609,32178876,44639341,

%U 60885140,81785221,108350264,141747321,183315176,234580425,297274276,373350069,465001516,574681661

%N Number of quadruples (p_1, ..., p_4) of positive integers such that p_{i-1} <= p_i <= n^(i-1).

%H Alois P. Heinz, <a href="/A354608/b354608.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F a(n) = (6*n^6-6*n^5+3*n^4+4*n^3-3*n^2+2*n)/6.

%F G.f.: x*(x^5+89*x^4+338*x^3+254*x^2+37*x+1)/(1-x)^7.

%e a(2) = 44: (1,1,1,1), (1,1,1,2), (1,1,1,3), (1,1,1,4), (1,1,1,5), (1,1,1,6), (1,1,1,7), (1,1,1,8), (1,1,2,2), (1,1,2,3), (1,1,2,4), (1,1,2,5), (1,1,2,6), (1,1,2,7), (1,1,2,8), (1,1,3,3), (1,1,3,4), (1,1,3,5), (1,1,3,6), (1,1,3,7), (1,1,3,8), (1,1,4,4), (1,1,4,5), (1,1,4,6), (1,1,4,7), (1,1,4,8), (1,2,2,2), (1,2,2,3), (1,2,2,4), (1,2,2,5), (1,2,2,6), (1,2,2,7), (1,2,2,8), (1,2,3,3), (1,2,3,4), (1,2,3,5), (1,2,3,6), (1,2,3,7), (1,2,3,8), (1,2,4,4), (1,2,4,5), (1,2,4,6), (1,2,4,7), (1,2,4,8).

%p a:= n-> (((((6*n-6)*n+3)*n+4)*n-3)*n+2)*n/6:

%p seq(a(n), n=0..30);

%Y Row n=4 of A355576.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Jul 08 2022