A252922 - OEIS

%I #43 May 04 2021 01:09:43

%S 0,1,4,8,14,17,25,26,35,36,46,43,58,54,66,62,79,73,88,77,101,94,110,

%T 92,120,115,133,113,138,126,158,134,167,143,165,150,193,177,189,154,

%U 206,188,228,182,224,206,234,198,244,229,274,222,263,224,272,246,312,272,290,230,318,290,326,262,327,315,355,296

%N a(n) = sigma(n-1) + sigma(n-2) + sigma(n-3), with a(1)=0, a(2)=1, a(3)=4.

%C This is also a rectangular array read by rows, with four columns, in which T(j,k) is the number of cells (also the area) of the j-th gap between the arms in the k-th quadrant of the spiral of the symmetric representation of sigma described in A239660, with j >= 1 and 1 <= k <= 4 and starting with T(1,1) = 0, see example.

%C We can find the spiral (mentioned above) on the terraces of the stepped pyramid described in A244050. - _Omar E. Pol_, Dec 07 2016

%H Robert Israel, <a href="/A252922/b252922.txt">Table of n, a(n) for n = 1..10000</a>

%F a(1) = 0, a(2) = sigma(1) = 1, a(3) = sigma(2) + sigma(1) = 4; for n >= 4, a(n) = sigma(n-1) + sigma(n-2) + sigma(n-3).

%F a(n) = A024916(n-1) - A024916(n-4) for n >= 5.

%e a(5) = sigma(4) + sigma(3) + sigma(2) = 7 + 4 + 3 = 14. On the other hand a(5) = A024916(4) - A024916(1) = 15 - 1 = 14.

%e ...

%e Also, if written as a rectangular array T(j,k) with four columns the sequence begins:

%e     0,   1,   4,   8;

%e    14,  17,  25,  26;

%e    35,  36,  46,  43;

%e    58,  54,  66,  62;

%e    79,  73,  88,  77;

%e   101,  94, 110,  92;

%e   120, 115, 133, 113;

%e   138, 126, 158, 134;

%e   167, 143, 165, 150;

%e   193, 177, 189, 154;

%e   206, 188, 228, 182;

%e   224, 206, 234, 198;

%e   244, 229, 274, 222;

%e   263, 224, 272, 246;

%e   312, 272, 290, 230;

%e   318, 290, 326, 262;

%e   ...

%e In this case T(2,1) = a(5) = 14.

%p L:= [0,0,0,seq(numtheory:-sigma(n), n=1..100)]:

%p L[1..101]+L[2..102]+L[3..103]; # _Robert Israel_, Dec 07 2016

%t a252922[n_] := Block[{f}, f[1] = 0; f[2] = 1; f[3] = 4;

%t   f[x_] := DivisorSigma[1, x - 1] + DivisorSigma[1, x - 2] +

%t DivisorSigma[1, x - 3]; Table[f[i], {i, n}]]; a252922[68] (* _Michael De Vlieger_, Dec 27 2014 *)

%o (PARI) v=concat([0,1,4],vector(100,n,sigma(n)+sigma(n+1)+sigma(n+2))) \\ _Derek Orr_, Dec 30 2014

%Y Cf. A000203, A010883, A024916, A092403, A112610, A193553, A196020, A236104, A237270, A237271, A237593, A239052, A239053, A239931-A239934, A239660, A240020, A244050, A245092, A262626.

%K nonn,tabf

%O 1,3

%A _Omar E. Pol_, Dec 24 2014