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A321391 Array read by antidiagonals: T(n,k) is the number of achiral rows of n colors using up to k colors. 7
1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 2, 1, 0, 1, 4, 3, 4, 1, 0, 1, 5, 4, 9, 4, 1, 0, 1, 6, 5, 16, 9, 8, 1, 0, 1, 7, 6, 25, 16, 27, 8, 1, 0, 1, 8, 7, 36, 25, 64, 27, 16, 1, 0, 1, 9, 8, 49, 36, 125, 64, 81, 16, 1, 0, 1, 10, 9, 64, 49, 216, 125, 256, 81, 32, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

The antidiagonals go from top-right to bottom-left.

LINKS

Table of n, a(n) for n=0..77.

FORMULA

T(n,k) = [n==0] + [n>0] * k^ceiling(n/2).

The generating function for column k is (1+k*x) / (1-k*x^2).

EXAMPLE

The array begins with T(0,0):

1 1  1   1    1     1     1      1      1      1       1       1 ...

0 1  2   3    4     5     6      7      8      9      10      11 ...

0 1  2   3    4     5     6      7      8      9      10      11 ...

0 1  4   9   16    25    36     49     64     81     100     121 ...

0 1  4   9   16    25    36     49     64     81     100     121 ...

0 1  8  27   64   125   216    343    512    729    1000    1331 ...

0 1  8  27   64   125   216    343    512    729    1000    1331 ...

0 1 16  81  256   625  1296   2401   4096   6561   10000   14641 ...

0 1 16  81  256   625  1296   2401   4096   6561   10000   14641 ...

0 1 32 243 1024  3125  7776  16807  32768  59049  100000  161051 ...

0 1 32 243 1024  3125  7776  16807  32768  59049  100000  161051 ...

0 1 64 729 4096 15625 46656 117649 262144 531441 1000000 1771561 ...

For T(3,3)=9, the rows are AAA, ABA, ACA, BAB, BBB, BCB, CAC, CBC, and CCC.

MATHEMATICA

Table[If[n>0, (n-k)^Ceiling[k/2], 1], {n, 0, 12}, {k, 0, n}] // Flatten

CROSSREFS

Columns 0-6 are A000007, A000012, A060546, A056449, A056450, A056451, A056452.

Cf. A003992 (oriented), A277504 (unoriented), A293500 (chiral).

Sequence in context: A301504 A307432 A256140 * A244003 A332670 A118344

Adjacent sequences:  A321388 A321389 A321390 * A321392 A321393 A321394

KEYWORD

nonn,easy,tabl

AUTHOR

Robert A. Russell, Nov 08 2018

STATUS

approved

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Last modified January 19 16:16 EST 2021. Contains 340270 sequences. (Running on oeis4.)