A252922 a(n) = sigma(n-1) + sigma(n-2) + sigma(n-3), with a(1)=0, a(2)=1, a(3)=4.

0, 1, 4, 8, 14, 17, 25, 26, 35, 36, 46, 43, 58, 54, 66, 62, 79, 73, 88, 77, 101, 94, 110, 92, 120, 115, 133, 113, 138, 126, 158, 134, 167, 143, 165, 150, 193, 177, 189, 154, 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

Offset

1,3

Comments

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.

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

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).

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

Example

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.
...
Also, if written as a rectangular array T(j,k) with four columns the sequence begins:
    0,   1,   4,   8;
   14,  17,  25,  26;
   35,  36,  46,  43;
   58,  54,  66,  62;
   79,  73,  88,  77;
  101,  94, 110,  92;
  120, 115, 133, 113;
  138, 126, 158, 134;
  167, 143, 165, 150;
  193, 177, 189, 154;
  206, 188, 228, 182;
  224, 206, 234, 198;
  244, 229, 274, 222;
  263, 224, 272, 246;
  312, 272, 290, 230;
  318, 290, 326, 262;
  ...
In this case T(2,1) = a(5) = 14.

Maple

L:= [0, 0, 0, seq(numtheory:-sigma(n), n=1..100)]:
L[1..101]+L[2..102]+L[3..103]; # Robert Israel, Dec 07 2016

Mathematica

a252922[n_] := Block[{f}, f[1] = 0; f[2] = 1; f[3] = 4;
  f[x_] := DivisorSigma[1, x - 1] + DivisorSigma[1, x - 2] +
DivisorSigma[1, x - 3]; Table[f[i], {i, n}]]; a252922[68] (* Michael De Vlieger, Dec 27 2014 *)

Prog

(PARI) v=concat([0, 1, 4], vector(100, n, sigma(n)+sigma(n+1)+sigma(n+2))) \\ Derek Orr, Dec 30 2014

Crossrefs

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

Sequence in context: A312396 A312397 A312398 * A312399 A312400 A333465

Adjacent sequences: A252919 A252920 A252921 * A252923 A252924 A252925

Keyword

nonn,tabf

Author

Omar E. Pol, Dec 24 2014

Status

approved