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Search: id:A122141
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| A122141 |
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Array: T(d,n) = number of ways of writing n as a sum of d squares, read along diagonals. |
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+0
3
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| 1, 1, 2, 1, 4, 0, 1, 6, 4, 0, 1, 8, 12, 0, 2, 1, 10, 24, 8, 4, 0, 1, 12, 40, 32, 6, 8, 0, 1, 14, 60, 80, 24, 24, 0, 0, 1, 16, 84, 160, 90, 48, 24, 0, 0, 1, 18, 112, 280, 252, 112, 96, 0, 4, 2, 1, 20, 144, 448, 574, 312, 240, 64, 12, 4, 0, 1, 22, 180, 672, 1136, 840, 544, 320, 24, 30, 8
(list; table; graph; listen)
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OFFSET
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1,3
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LINKS
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Index entries for sequences related to sums of squares
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FORMULA
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T(1,n)=A000122(n); T(2,n)=A004018(n); T(3,n)=A005875(n); T(4,n)=A000118(n); T(5,n)=A000132(n); T(6,n)=A000141(n); T(7,n)=A008451(n); T(8,n)=A000143(n); T(9,n)=A008452(n); T(10,n)=A000144(n); T(d,0)=1; T(d,1)=A005843(d); T(d,2)=A046092(d).
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EXAMPLE
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Array T(d,n) with rows d=1,2,3... and columns n=0,1,2,3.. reads
1 2 0 0 2 0 0 0 0 2 0 ...
1 4 4 0 4 8 0 0 4 4 8 ...
1 6 12 8 6 24 24 0 12 30 24 ...
1 8 24 32 24 48 96 64 24 104 144 ...
1 10 40 80 90 112 240 320 200 250 560 ...
1 12 60 160 252 312 544 960 1020 876 1560 ...
1 14 84 280 574 840 1288 2368 3444 3542 4424 ...
1 16 112 448 1136 2016 3136 5504 9328 12112 14112 ...
1 18 144 672 2034 4320 7392 12672 22608 34802 44640 ...
1 20 180 960 3380 8424 16320 28800 52020 88660 129064
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MAPLE
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T := proc(d, n) local i, cnts ; cnts := 0 ; for i from -trunc(sqrt(n)) to trunc(sqrt(n)) do if n-i^2 >= 0 then if d > 1 then cnts := cnts+T(d-1, n-i^2) ; elif n-i^2 = 0 then cnts := cnts+1 ; fi ; fi ; od ; RETURN(cnts) ; end: for diag from 1 to 14 do for n from 0 to diag-1 do d := diag-n ; printf("%d, ", T(d, n)) ; od ; od;
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CROSSREFS
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Adjacent sequences: A122138 A122139 A122140 this_sequence A122142 A122143 A122144
Sequence in context: A016585 A143316 A127192 this_sequence A091604 A137629 A087569
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KEYWORD
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nonn,tabl
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 29 2006
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