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A277504 Array a(n, k) giving the number of reversible strings with n beads of k colors, read by antidiagonals. 12
1, 2, 1, 3, 3, 1, 4, 6, 6, 1, 5, 10, 18, 10, 1, 6, 15, 40, 45, 20, 1, 7, 21, 75, 136, 135, 36, 1, 8, 28, 126, 325, 544, 378, 72, 1, 9, 36, 196, 666, 1625, 2080, 1134, 136, 1, 10, 45, 288, 1225, 3996, 7875, 8320, 3321, 272, 1, 11, 55, 405, 2080, 8575, 23436, 39375, 32896, 9963, 528, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

See A005418.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1275

FORMULA

a(n,k) = (k^n + k^((n + mod(n,2))/2))/2.

EXAMPLE

Array begins:

1   2     3      4       5       6          7         8 ...

1   3     6     10      15      21         28        36 ...

1   6    18     40      75     126        196       288 ...

1  10    45    136     325     666       1225      2080 ...

1  20   135    544    1625    3996       8575     16640 ...

1  36   378   2080    7875   23436      58996    131328 ...

1  72  1134   8320   39375  140616     412972   1050624 ...

1 136  3321  32896  195625  840456    2883601   8390656 ...

1 272  9963 131584  978125  5042736  20185207  67125248 ...

1 528 29646 524800 4884375 30236976 141246028 536887296 ...

...

MATHEMATICA

a[k_, n_] :=  (k^n + k^((n + Mod[n, 2])/2))/2; Table[a[k - n + 1, n], {k, 1, 12}, {n, 1, k}] // Flatten

CROSSREFS

Columns 2-6 are A005418, A032120, A032121, A032122, A056308.

Rows 2-6 are A000217 (triangular numbers), A002411 (pentagonal pyramidal numbers), A037270, A168178, A071232.

Transpose is A284979.

Cf. A284871, A284949.

Sequence in context: A192001 A122176 A159881 * A098546 A126277 A253273

Adjacent sequences:  A277501 A277502 A277503 * A277505 A277506 A277507

KEYWORD

nonn,tabl

AUTHOR

Jean-Fran├žois Alcover, Oct 18 2016

EXTENSIONS

Transposed array for greater consistency. - Andrew Howroyd, Apr 04 2017

STATUS

approved

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Last modified February 19 10:31 EST 2018. Contains 299330 sequences. (Running on oeis4.)