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A236112 Triangle read by rows: T(n,k), n>=1, k>=1, in which column k lists k+1 copies of the squares in nondecreasing order, and the first element of column k is in row k(k+1)/2. 16
0, 0, 1, 0, 1, 0, 4, 0, 4, 1, 0, 9, 1, 0, 9, 1, 0, 16, 4, 0, 16, 4, 1, 0, 25, 4, 1, 0, 25, 9, 1, 0, 36, 9, 1, 0, 36, 9, 4, 0, 49, 16, 4, 1, 0, 49, 16, 4, 1, 0, 64, 16, 4, 1, 0, 64, 25, 9, 1, 0, 81, 25, 9, 1, 0, 81, 25, 9, 4, 0, 100, 36, 9, 4, 1, 0, 100, 36, 16, 4, 1, 0, 121, 36, 16, 4, 1, 0, 121, 49, 16, 4, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Gives an identity for the sum of remainders of n mod k, for k = 1,2,3,...,n. Alternating sum of row n equals A004125(n), i.e., sum_{k=1..A003056(n))} (-1)^(k-1)*T(n,k) = A004125(n).

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..94.

EXAMPLE

Triangle begins:

0;

0;

1,     0;

1,     0;

4,     0;

4,     1,   0;

9,     1,   0;

9,     1,   0;

16,    4,   0;

16,    4,   1,   0;

25,    4,   1,   0;

25,    9,   1,   0;

36,    9,   1,   0;

36,    9,   4,   0;

49,   16,   4,   1,  0;

49,   16,   4,   1,  0;

64,   16,   4,   1,  0;

64,   25,   9,   1,  0;

81,   25,   9,   1,  0;

81,   25,   9,   4,  0;

100,  36,   9,   4,  1,  0;

100,  36,  16,   4,  1,  0;

121,  36,  16,   4,  1,  0;

121,  49,  16,   4,  1,  0;

...

For n = 24 the 24th row of triangle is 121, 49, 16, 4, 1, 0 therefore the alternating row sum is 121 - 49 + 16 - 4 + 1 - 0 = 85 equaling A004125(24).

CROSSREFS

Cf. A000203, A000217, A000290, A003056, A004125, A120444, A196020, A211343, A228813, A231345, A231347, A235791, A235794, A236104, A236106, A237048, A237591, A237593, A261699.

Sequence in context: A019201 A137660 A123583 * A226787 A140574 A010636

Adjacent sequences:  A236109 A236110 A236111 * A236113 A236114 A236115

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Jan 23 2014

STATUS

approved

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Last modified September 16 10:36 EDT 2019. Contains 327094 sequences. (Running on oeis4.)