A236631 - OEIS

A236631

Triangle read by rows: T(j,k), j>=1, k>=1, in which column k lists the positive squares repeated k-1 times, except the column 1 which is A123327. The elements of the even-indexed columns are multiplied by -1. The first element of column k is in row k(k+1)/2.

1, 3, 5, -1, 8, -1, 10, -4, 15, -4, 1, 16, -9, 1, 23, -9, 1, 25, -16, 4, 31, -16, 4, -1, 34, -25, 4, -1, 45, -25, 9, -1, 42, -36, 9, -1, 55, -36, 9, -4, 60, -49, 16, -4, 1, 67, -49, 16, -4, 1, 69, -64, 16, -4, 1, 86, -64, 25, -9, 1, 84, -81, 25, -9, 1, 103

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OFFSET

1,2

COMMENTS

T(j,k) which row j has length A003056(j) hence the first element of column k is in row A000217(j).

Row sums give A000203.

Interpreted as a sequence with index n this is also the first differences of A236630. If a(n) is positive then a(n) is the number of cells turned ON at n-th stage in the structure of A236630. If a(n) is negative then a(n) is the number of cells turned OFF at n-th stage in the structure of A236630.

LINKS

Table of n, a(n) for n=1..66.

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to sigma(n)

FORMULA

T(n,1) = A000203(n) + A004125(n).

EXAMPLE

Written as an irregular triangle the sequence begins:

5, -1;

8, -1;

10, -4;

15, -4, 1;

16, -9, 1;

23, -9, 1;

25, -16, 4;

31, -16, 4, -1;

34, -25, 4, -1;

45, -25, 9, -1;

42, -36, 9, -1;

55, -36, 9, -4;

60, -49, 16, -4, 1;

67, -49, 16, -4, 1;

69, -64, 16, -4, 1;

86, -64, 25, -9, 1;

84, -81, 25, -9, 1;

103, -81, 25, -9, 4;

102, -100, 36, -9, 4, -1;

113, -100, 36, -16, 4, -1;

122, -121, 36, -16, 4, -1;

145, -121, 49, -16, 4, -1;

...

For j = 15 the divisors of 15 are 1, 3, 5, 15, therefore the sum of divisors of 15 is 1 + 3 + 5 + 15 = 24. On the other hand the 15th row of triangle is 60, -49, 16, -4, 1, therefore the row sum is 60 - 49 + 16 - 4 + 1 = 24, equalling the sum of divisors of 15.

CROSSREFS

Cf. A000203, A000217, A000290, A003056, A004125, A024916, A008794, A123327, A196020, A211547, A236104, A236630, A237593.

Sequence in context: A367743 A242390 A065395 * A302800 A367067 A340529

Adjacent sequences: A236628 A236629 A236630 * A236632 A236633 A236634

KEYWORD

sign,tabf

AUTHOR

Omar E. Pol, Jan 29 2014

STATUS

approved