This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A224366 Number of compositions of n^2 into sums of squares. 8
 1, 1, 2, 11, 124, 2870, 133462, 12477207, 2344649612, 885591183971, 672331353833716, 1025954712063362545, 3146790000180780110540, 19400015532276248131470280, 240398159948843792847457589388, 5987629866666297470033540284817068, 299759874416459708067727376075503706332 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Equals the row sums of triangle A232266. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..81 FORMULA a(n) = [x^(n^2)] 1/(1 - Sum_{k>=1} x^(k^2)). a(n) = A006456(n^2). a(n) = Sum_{k=1..n} A006456(n^2-k^2) for n>=1 with a(0)=1. EXAMPLE Illustrate a(n) = Sum_{k=1..n} A006456(n^2-k^2): a(1) = 1 = 1; a(2) = 2 = 1 + 1; a(3) = 11 = 7 + 3 + 1; a(4) = 124 = 88 + 30 + 5 + 1; a(5) = 2870 = 2024 + 710 + 124 + 11 + 1; a(6) = 133462 = 94137 + 33033 + 5767 + 502 + 22 + 1; a(7) = 12477207 = 8800750 + 3088365 + 539192 + 46832 + 2024 + 43 + 1; ... MAPLE b:= proc(n) option remember; local i; if n=0 then 1       else 0; for i while i^2<=n do %+b(n-i^2) od fi     end: a:= n-> b(n^2): seq(a(n), n=0..17);  # Alois P. Heinz, Aug 12 2017 MATHEMATICA b[0] = 1; b[n_] := b[n] = Sum[b[n-k], {k, Select[Range[n], IntegerQ[ Sqrt[#]]&]}]; a[n_] := b[n^2]; Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Jun 09 2018 *) PROG (PARI) {a(n)=polcoeff(1/(1-sum(k=1, n, x^(k^2))+x*O(x^(n^2))), n^2)} for(n=0, 21, print1(a(n), ", ")) (PARI) {A006456(n)=polcoeff(1/(1-sum(k=1, sqrtint(n+1), x^(k^2))+x*O(x^n)), n)} {a(n)=if(n==0, 1, sum(k=1, n, A006456(n^2-k^2)))} for(n=0, 21, print1(a(n), ", ")) CROSSREFS Cf. A006456, A232266. Sequence in context: A001946 A121337 A269069 * A279703 A206401 A193207 Adjacent sequences:  A224363 A224364 A224365 * A224367 A224368 A224369 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 05 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)