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A210843 Level of the n-th plateau of the column k of the square array A195825, when k -> infinity. 16
1, 4, 13, 35, 86, 194, 415, 844, 1654, 3133, 5773, 10372, 18240, 31449, 53292, 88873, 146095, 236977, 379746, 601656, 943305, 1464501, 2252961, 3436182, 5198644, 7805248, 11634685, 17224795, 25336141, 37038139, 53828275, 77792869 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also the first (k+1)/2 terms of this sequence are the levels of the (k+1)/2 plateaus of the column k of A195825, whose lengths are k+1, k-1, k-3, k-5,... 2, if k is odd.

Also the first k/2 terms of this sequence are the levels of the k/2 plateaus of the column k of A195825, whose lengths are k+1, k-1, k-3, k-5,... 3, if k is a positive even number.

For the visualization of the plateaus see the graph of the sequences mentioned in crossrefs section (columns k=1..10 of A195825), for example see the graph of A210964.

Also numbers that are repeated in column k of square array A195825, when k -> infinity.

Note that the definition and the comments related to the square array A195825 mentioned above are also valid for the square array A211970, since both arrays contains the same columns, if k >= 1.

Is this the EULER transform of 4, 3, 3, 3, 3, 3, 3...?

LINKS

Table of n, a(n) for n=1..32.

FORMULA

From Vaclav Kotesovec, Aug 16 2015: (Start)

a(n) ~ sqrt(2*n)/Pi * A000716(n).

a(n) ~ exp(sqrt(2*n)*Pi) / (8*Pi*n).

(End)

EXAMPLE

Column 1 of A195825 is A000041 which starts: [1, 1], 2, 3, 5, 7, 11... The column contains only one plateau: [1, 1] which has level 1 and length 2. So a(1) = 1.

Column 3 of A195825 is A036820 which starts: [1, 1, 1, 1], 2, 3, [4, 4], 5, 7, 10... The column contains only two plateaus: [1, 1, 1, 1], [4, 4], which have levels 1, 4 and lengths 4, 2. So a(1)= 1 and a(2) = 2.

Column 6 of A195825 is A195850 which starts: [1, 1, 1, 1, 1, 1, 1], 2, 3, [4, 4, 4, 4, 4], 5, 7, 10, 12, [13, 13, 13], 14, 16, 21... The column contains three plateaus: [1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4], [13, 13, 13], which have levels 1, 4, 13 and lengths 7, 5, 3. So a(1) = 1, a(2) = 4 and a(3) = 13.

MATHEMATICA

CoefficientList[Series[1/(1-x)*Product[1/(1-x^k)^3, {k, 1, 50}], {x, 0, 50}], x] (* Vaclav Kotesovec, Aug 16 2015 *)

PROG

(GWBASIC).

10 'This program gives the 32 terms of DATA section.

20 'Suppose that we have A057077().

30 'In this case g(n) is the n-th generalized 64-gonal number.

40 DEFDBL a, g, w

50 DIM a(32), A057077(2079), g(2080), w(2079)

60 n=0: w(0)=1

70 FOR i = 1 TO 2079

80   FOR j = 1 TO i

90     IF g(j)<=i THEN w(i)=w(i)+A057077(j-1)*w(i-g(j))

100   NEXT j

110  IF i=1 GOTO 130

120  IF w(i-2)=w(i-1) AND w(i-1)<>a(n) THEN n=n+1: a(n)=w(i-1): PRINT a(n);

130 NEXT i

140 END

CROSSREFS

Partial sums of A000716. Column 3 of A210764.

Columns (k=1..10) of A195825: A000041, A006950, A036820, A195848, A195849, A195850, A195851, A195852, A196933, A210964.

Cf. A000070, A000712, A000713, A010815, A211970.

Sequence in context: A189588 A266357 A095941 * A177155 A189595 A189602

Adjacent sequences:  A210840 A210841 A210842 * A210844 A210845 A210846

KEYWORD

nonn

AUTHOR

Omar E. Pol, Jun 19 2012

STATUS

approved

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Last modified February 22 12:33 EST 2020. Contains 332136 sequences. (Running on oeis4.)