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A286815 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of (Product_{j>=1} (1 - x^(2*j))^5/((1 - x^j)*(1 - x^(4*j)))^2)^k. 21
1, 1, 0, 1, 2, 0, 1, 4, 0, 0, 1, 6, 4, 0, 0, 1, 8, 12, 0, 2, 0, 1, 10, 24, 8, 4, 0, 0, 1, 12, 40, 32, 6, 8, 0, 0, 1, 14, 60, 80, 24, 24, 0, 0, 0, 1, 16, 84, 160, 90, 48, 24, 0, 0, 0, 1, 18, 112, 280, 252, 112, 96, 0, 4, 2, 0, 1, 20, 144, 448, 574, 312, 240, 64, 12 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A(n,k) is the number of ways of writing n as a sum of k squares.

This is the transpose of the array in A122141.

LINKS

Seiichi Manyama, Antidiagonals n = 0..139, flattened

FORMULA

G.f. of column k: (Product_{j>=1} (1 - x^(2*j))^5/((1 - x^j)*(1 - x^(4*j)))^2)^k.

EXAMPLE

Square array begins:

   1, 1, 1,  1,  1, ...

   0, 2, 4,  6,  8, ...

   0, 0, 4, 12, 24, ...

   0, 0, 0,  8, 32, ...

   0, 2, 4,  6, 24, ...

MAPLE

A:= proc(n, k) option remember; `if`(n=0, 1, `if`(n<0 or k<1, 0,

      A(n, k-1) +2*add(A(n-j^2, k-1), j=1..isqrt(n))))

    end:

seq(seq(A(n, d-n), n=0..d), d=0..12);  # Alois P. Heinz, May 27 2017

CROSSREFS

Columns k=0-13 give: A000007, A000122, A004018, A005875, A000118, A000132, A000141, A008451, A000143, A008452, A000144, A008453, A000145, A276285.

Diagonal gives A066535.

Cf. A122141.

Sequence in context: A152837 A182036 A174996 * A256276 A257920 A258210

Adjacent sequences:  A286812 A286813 A286814 * A286816 A286817 A286818

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, May 27 2017

STATUS

approved

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Last modified February 21 02:19 EST 2018. Contains 299388 sequences. (Running on oeis4.)