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A262612 Triangle read by rows T(n,k) in which column k lists the partial sums of the k-th column of triangle A236104. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 16 04:49 EDT 2021. Contains 343030 sequences. (Running on oeis4.)