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A206772 Table T(n,k)=max{4*n+k-4,n+4*k-4} n, k > 0, read by antidiagonals. 3
1, 5, 5, 9, 6, 9, 13, 10, 10, 13, 17, 14, 11, 14, 17, 21, 18, 15, 15, 18, 21, 25, 22, 19, 16, 19, 22, 25, 29, 26, 23, 20, 20, 23, 26, 29, 33, 30, 27, 24, 21, 24, 27, 30, 33, 37, 34, 31, 28, 25, 25, 28, 31, 34, 37, 41, 38, 35, 32, 29, 26, 29, 32, 35, 38, 41, 45 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In general, let m be natural number. Table T(n,k)=max{m*n+k-m,n+m*k-m}. For m=1 the result is A002024, for m=2 the result is A204004, for m=3 the result is A204008. This sequence is result for m=4.

LINKS

Boris Putievskiy, Rows n = 1..140 of triangle, flattened

Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO]

FORMULA

For the general case

a(n) = m*A002024(n) + (m-1)*max{-A002260(n),-A004736(n)}.

a(n) = m*(t+1) + (m-1)*max{t*(t+1)/2-n,n-(t*t+3*t+4)/2}

where t=floor((-1+sqrt(8*n-7))/2).

For m=4

a(n) = 4*(t+1) + 3*max{t*(t+1)/2-n,n-(t*t+3*t+4)/2}

where t=floor((-1+sqrt(8*n-7))/2).

EXAMPLE

The start of the sequence as table for general case:

1........m+1..2*m+1..3*m+1..4*m+1..5*m+1..6*m+1 ...

m+1......m+2..2*m+2..3*m+2..4*m+2..5*m+2..6*m+2 ...

2*m+1..2*m+2..2*m+3..3*m+3..4*m+3..5*m+3..6*m+3 ...

3*m+1..3*m+2..3*m+3..3*m+4..4*m+4..5*m+4..6*m+4 ...

4*m+1..4*m+2..4*m+3..4*m+4..4*m+5..5*m+5..6*m+5 ...

5*m+1..5*m+2..5*m+3..5*m+4..5*m+5..5*m+6..6*m+6 ...

6*m+1..6*m+2..6*m+3..6*m+4..6*m+5..6*m+6..6*m+7 ...

. . .

The start of the sequence as triangle array read by rows for general case:

1;

m+1, m+1;

2*m+1, m+2, 2*m+1;

3*m+1, 2*m+2, 2*m+2, 3*m+1;

4*m+1, 3*m+2, 2*m+3, 3*m+2, 4*m+1;

5*m+1, 4*m+2, 3*m+3, 2*m+4, 3*m+3, 4*m+2; 5*m+1;

6*m+1, 5*m+2, 4*m+3, 3*m+4, 2*m+5, 3*m+4, 4*m+3; 5*m+2, 6*m+1;

. . .

Row number r contains r numbers: r*m+1, (r-1)*m+2, ... (r-1)*m+2, r*m+1.

PROG

(Python)

t=int((math.sqrt(8*n-7)-1)/2)

result=4*(t+1)+3*max(t*(t+1)/2-n, n-(t*t+3*t+4)/2)

CROSSREFS

Cf. A002024, A204004, A204008, A002260, A004736.

Sequence in context: A030798 A331502 A021951 * A200679 A124175 A168277

Adjacent sequences: A206769 A206770 A206771 * A206773 A206774 A206775

KEYWORD

nonn,tabl

AUTHOR

Boris Putievskiy, Jan 15 2013

STATUS

approved

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Last modified November 30 02:32 EST 2022. Contains 358431 sequences. (Running on oeis4.)