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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. 26
 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 MATHEMATICA A[n_, k_] := A[n, k] = If[n == 0, 1, If[n < 0 || k < 1, 0, A[n, k-1] + 2*Sum[A[n-j^2, k-1], {j, 1, Sqrt[n]}]]]; Table[A[n, d-n], {d, 0, 12}, {n, 0, d}] // Flatten (* Jean-François Alcover, Feb 28 2018, after Alois P. Heinz *) CROSSREFS Columns k=0-16 give: A000007, A000122, A004018, A005875, A000118, A000132, A000141, A008451, A000143, A008452, A000144, A008453, A000145, A276285, A276286, A276287, A000152. 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 December 17 12:20 EST 2018. Contains 318201 sequences. (Running on oeis4.)