A262612 Triangle read by rows T(n,k) in which column k lists the partial sums of the k-th column of triangle A236104.

1, 5, 14, 1, 30, 2, 55, 6, 91, 10, 1, 140, 19, 2, 204, 28, 3, 285, 44, 7, 385, 60, 11, 1, 506, 85, 15, 2, 650, 110, 24, 3, 819, 146, 33, 4, 1015, 182, 42, 8, 1240, 231, 58, 12, 1, 1496, 280, 74, 16, 2, 1785, 344, 90, 20, 3, 2109, 408, 115, 29, 4, 2470, 489, 140, 38, 5, 2870, 570, 165, 47, 9, 3311, 670, 201, 56, 13, 1

Offset

1,2

Comments

Alternating sum of row n equals A175254(n), i.e., sum_{k=1..A003056(n))} (-1)^(k-1)*T(n,k) = A175254(n), which is also the volume (or the total number of units cubes) in the first n levels of the stepped pyramid described in A245092.

Row n has length A003056(n) hence the first element of column k is in row A000217(k).

Links

Table of n, a(n) for n=1..76.

Example

Triangle begins:
     1;
     5;
    14,    1;
    30,    2;
    55,    6;
    91,   10,    1;
   140,   19,    2;
   204,   28,    3;
   285,   44,    7;
   385,   60,   11,    1;
   506,   85,   15,    2;
   650,  110,   24,    3;
   819,  146,   33,    4;
  1015,  182,   42,    8;
  1240,  231,   58,   12,    1;
  1496,  280,   74,   16,    2;
  1785,  344,   90,   20,    3;
  2109,  408,  115,   29,    4;
  2470,  489,  140,   38,    5;
  2870,  570,  165,   47,    9;
  3311,  670,  201,   56,   13,    1;
  3795,  770,  237,   72,   17,    2;
  4324,  891,  273,   88,   21,    3;
  4900, 1012,  322,  104,   25,    4;
  ...
For n = 6 we have that A175254(6) = [1] + [1 + 3] + [1 + 3 + 4] + [1 + 3 + 4 + 7] + [1 + 3 + 4 + 7 + 6] + [1 + 3 + 4 + 7 + 6 + 12] = 1 + 4 + 8 + 15 + 21 + 33 = 82. On the other hand the alternating sum of the 6th row of the triangle is 91 - 10 + 1 = 82, equaling A175254(6).

Crossrefs

Cf. A000203, A000217, A003056, A024916, A175254, A196020, A235791, A236104, A237048, A237591, A237593, A237270, A237271, A245092, A261699, A262626.

Column 1 gives A000330, n >= 1. Column 2 is A005993. It appears that column 3 is A092353.

Sequence in context: A127317 A049506 A069524 * A333025 A144518 A051542

Adjacent sequences: A262609 A262610 A262611 * A262613 A262614 A262615

Keyword

nonn,tabf

Author

Omar E. Pol, Nov 03 2015

Status

approved