A379220 Square array A(n, k) = sigma((2n-1)^2) * sigma((2k-1)^2), read by antidiagonals.

1, 13, 13, 31, 169, 31, 57, 403, 403, 57, 121, 741, 961, 741, 121, 133, 1573, 1767, 1767, 1573, 133, 183, 1729, 3751, 3249, 3751, 1729, 183, 403, 2379, 4123, 6897, 6897, 4123, 2379, 403, 307, 5239, 5673, 7581, 14641, 7581, 5673, 5239, 307, 381, 3991, 12493, 10431, 16093, 16093, 10431, 12493, 3991, 381, 741, 4953, 9517, 22971, 22143, 17689, 22143, 22971, 9517, 4953, 741

Offset: 1

Author

Antti Karttunen, Dec 22 2024

Keywords

• nonn
• tabl

Comments

Array is symmetric.

Examples

			The top left corner of the array:
   n\k   |    1      2      3      4       5       6       7       8       9
(*2-1)^2 |    1      9     25     49      81     121     169     225     289
---------+-------------------------------------------------------------------
   1   1 |    1,    13,    31,    57,    121,    133,    183,    403,    307,
   2   9 |   13,   169,   403,   741,   1573,   1729,   2379,   5239,   3991,
   3  25 |   31,   403,   961,  1767,   3751,   4123,   5673,  12493,   9517,
   4  49 |   57,   741,  1767,  3249,   6897,   7581,  10431,  22971,  17499,
   5  81 |  121,  1573,  3751,  6897,  14641,  16093,  22143,  48763,  37147,
   6 121 |  133,  1729,  4123,  7581,  16093,  17689,  24339,  53599,  40831,
   7 169 |  183,  2379,  5673, 10431,  22143,  24339,  33489,  73749,  56181,
   8 225 |  403,  5239, 12493, 22971,  48763,  53599,  73749, 162409, 123721,
   9 289 |  307,  3991,  9517, 17499,  37147,  40831,  56181, 123721,  94249,
  10 361 |  381,  4953, 11811, 21717,  46101,  50673,  69723, 153543, 116967,
  11 441 |  741,  9633, 22971, 42237,  89661,  98553, 135603, 298623, 227487,
  12 529 |  553,  7189, 17143, 31521,  66913,  73549, 101199, 222859, 169771,
  13 625 |  781, 10153, 24211, 44517,  94501, 103873, 142923, 314743, 239767,
  14 729 | 1093, 14209, 33883, 62301, 132253, 145369, 200019, 440479, 335551,
  15 841 |  871, 11323, 27001, 49647, 105391, 115843, 159393, 351013, 267397,
  16 961 |  993, 12909, 30783, 56601, 120153, 132069, 181719, 400179, 304851,
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A016754.

Cf. A379223 (the first row and the first column).

Cf. also A379221.

Programs

PARI

up_to = 66;
A379220sq(x,y) = (sigma((x+x-1)^2) * sigma((y+y-1)^2));
A379220list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A379220sq(col,(a-(col-1))))); (v); };
v379220 = A379220list(up_to);
A379220(n) = v379220[n];

Formula

A(n, k) = A379223(n) * A379223(k).

A(n, k) = A000203(A016754(n-1)) * A000203(A016754(k-1)). [NB: A016754 uses 0-based indexing]