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A255195 Triangle describing the shape of one eighth of the Gauss circle problem. 4
1, 2, 0, 2, 1, 0, 2, 1, 1, 0, 2, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 1, 0, 0, 2, 1, 1, 2, 2, 0, 0, 0, 2, 1, 1, 2, 1, 2, 0, 0, 0, 2, 1, 1, 1, 2, 2, 1, 0, 0, 0, 2, 1, 1, 1, 2, 1, 2, 1, 0, 0, 0, 2, 1, 1, 1, 2, 1, 2, 2, 0, 0, 0, 0, 2, 1, 1, 1, 2, 1, 2, 2, 1, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sum of terms of row n is n.

Total of partial sums in reverse (from right to left) equals one eighth of the Gauss circle problem. Whenever there is the number 2 the border of the circle makes a jump upwards. Predicting where the 2s are would say something about the Gauss circle problem. The number of 2s equals the number of 0s in the same row, and is counted by A194920(n-1).

LINKS

Table of n, a(n) for n=1..91.

E. W. Weisstein, Gauss's Circle Problem

FORMULA

A000603(n) = 2*(Sum_{k=1..n} Sum_{k=1..k} T(n,n-k+1))-ceiling((n-1)/sqrt(2)) for n>1.

A247588(n-1) = (Sum_{k=1..n} Sum_{k=1..k} (T(n,k) - T(n,n-k+1))/2).

EXAMPLE

1,

2, 0,

2, 1, 0,

2, 1, 1, 0,

2, 1, 2, 0, 0,

2, 1, 1, 2, 0, 0,

2, 1, 1, 2, 1, 0, 0,

2, 1, 1, 2, 2, 0, 0, 0,

2, 1, 1, 2, 1, 2, 0, 0, 0,

2, 1, 1, 1, 2, 2, 1, 0, 0, 0,

2, 1, 1, 1, 2, 1, 2, 1, 0, 0, 0,

2, 1, 1, 1, 2, 1, 2, 2, 0, 0, 0, 0,

2, 1, 1, 1, 2, 1, 2, 2, 1, 0, 0, 0, 0

MATHEMATICA

Flatten[Table[Sum[Table[If[And[If[n^2 + k^2 <= r^2, If[n >= k, 1, 0], 0] == 1, If[(n + 1)^2 + (k + 1)^2 <= r^2, If[n >= k, 1, 0], 0]== 0], 1, 0], {k, 0, r}], {n, 0, r}], {r, 0, 12}]]

CROSSREFS

Cf. A000603, A194920.

Sequence in context: A035394 A321101 A067167 * A194317 A096810 A190436

Adjacent sequences:  A255192 A255193 A255194 * A255196 A255197 A255198

KEYWORD

nonn,tabl

AUTHOR

Mats Granvik, Feb 16 2015

STATUS

approved

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Last modified August 22 05:00 EDT 2019. Contains 326172 sequences. (Running on oeis4.)