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A177121 Square array T(n,k) read by antidiagonals up: T(n,k) = 1 if n=1; otherwise if n divides k then T(n,k) = -n+1; otherwise T(n,k) = 1. 4
1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -2, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -3, 1, -1, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, 1, -4, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -5, 1, -3, -2, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -6, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,13

COMMENTS

Replace the first column in A077049 with any k-th column in A177121 (this array) to get a new array. Then the matrix inverse of the new array will have the k-th column of A054535 (Ramanujan sum) as its first column.

Obtained from A176079 by transposing, flipping signs, and adding a lower triangle of all -1's. - R. J. Mathar, Jul 08 2011

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65703 (the first 362 antidiagonals of array)

FORMULA

T(n,k) = 1 if n=1; otherwise, if n divides k then T(n,k) = -n+1; otherwise T(n,k) = 1.

EXAMPLE

Table begins:

  1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...

  1, -1,  1, -1,  1, -1,  1, -1,  1, -1, ...

  1,  1, -2,  1,  1, -2,  1,  1, -2,  1, ...

  1,  1,  1, -3,  1,  1,  1, -3,  1,  1, ...

  1,  1,  1,  1, -4,  1,  1,  1,  1, -4, ...

  1,  1,  1,  1,  1, -5,  1,  1,  1,  1, ...

  1,  1,  1,  1,  1,  1, -6,  1,  1,  1, ...

  1,  1,  1,  1,  1,  1,  1, -7,  1,  1, ...

  1,  1,  1,  1,  1,  1,  1,  1, -8,  1, ...

  1,  1,  1,  1,  1,  1,  1,  1,  1, -9, ...

  ...

PROG

(Excel) =if(row()=1; 1; if(mod(column(); row())=0; -row()+1; 1))

(PARI)

up_to = 65703; \\ = binomial(362+1, 2)

A177121sq(row, col) = if(1==row, 1, if(!(col%row), (1-row), 1));

A177121list(up_to) = { my(v = vector(up_to), i=0); for(a=1, oo, for(col=1, a, if(i++ > up_to, return(v)); v[i] = A177121sq((a-(col-1)), col))); (v); };

v177121 = A177121list(up_to);

A177121(n) = v177121[n]; \\ Antti Karttunen, Sep 25 2018

CROSSREFS

Cf. A051731, A054535, A077049, A176079.

Sequence in context: A146291 A327538 A086251 * A329314 A092931 A147300

Adjacent sequences:  A177118 A177119 A177120 * A177122 A177123 A177124

KEYWORD

sign,tabl,look

AUTHOR

Mats Granvik and Gary W. Adamson, May 03 2010

STATUS

approved

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Last modified February 28 01:55 EST 2020. Contains 332319 sequences. (Running on oeis4.)