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 A298640 Number of compositions (ordered partitions) of n^2 into squares > 1. 4
 1, 0, 1, 1, 2, 8, 12, 129, 874, 9630, 167001, 3043147, 72844510, 2423789655, 106665874384, 6156805673648, 470151743582651, 47558937432498729, 6363358599941131580, 1126147544855148769425, 263646401550138303553708, 81649922556593759124887197 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..128 FORMULA a(n) = [x^(n^2)] 1/(1 - Sum_{k>=2} x^(k^2)). a(n) = A280542(A000290(n)). EXAMPLE a(5) = 8 because we have [25], [16, 9], [9, 16], [9, 4, 4, 4, 4], [4, 9, 4, 4, 4], [4, 4, 9, 4, 4], [4, 4, 4, 9, 4] and [4, 4, 4, 4, 9]. MAPLE b:= proc(n) option remember; `if`(n=0, 1,       add(b(n-j^2), j=2..isqrt(n)))     end: a:= n-> b(n^2): seq(a(n), n=0..25);  # Alois P. Heinz, Feb 05 2018 MATHEMATICA b[n_] := b[n] = If[n == 0, 1, Sum[b[n - j^2], {j, 2, Floor @ Sqrt[n]}]]; a[n_] := b[n^2]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 21 2018, after Alois P. Heinz *) CROSSREFS Cf. A000290, A006456, A078134, A224366, A280542, A298642. Sequence in context: A330816 A066471 A001229 * A120000 A067678 A134905 Adjacent sequences:  A298637 A298638 A298639 * A298641 A298642 A298643 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jan 24 2018 STATUS approved

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Last modified June 4 08:18 EDT 2020. Contains 334825 sequences. (Running on oeis4.)