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Search: id:A094728
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| A094728 |
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Triangle read by rows: T(n,k) = n^2 - k^2, 0<=k<n. |
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+0
5
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| 1, 4, 3, 9, 8, 5, 16, 15, 12, 7, 25, 24, 21, 16, 9, 36, 35, 32, 27, 20, 11, 49, 48, 45, 40, 33, 24, 13, 64, 63, 60, 55, 48, 39, 28, 15, 81, 80, 77, 72, 65, 56, 45, 32, 17, 100, 99, 96, 91, 84, 75, 64, 51, 36, 19, 121, 120, 117, 112, 105, 96, 85, 72, 57, 40, 21, 144
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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T(n,0)=A000290(n); T(n,1)=A005563(n-1) for n>1; T(n,2)=A028347(n) for n>2; T(n,3)=A028560(n-3) for n>3; T(n,4)=A028566(n-4) for n>4;
T(n,n-1)=A005408(n); T(n,n-2)=A008586(n-1) for n>1; T(n,n-3)=A016945(n-2) for n>2; T(n,n-4)=A008590(n-2) for n>3; T(n,n-5)=A017329(n-3) for n>4; T(n,n-6)=A008594(n-3) for n>5; T(n,n-8)=A008598(n-2) for n>7;
T(A005408(k),k) = A000567(k);
row sums give A002412;
(T(n,k) mod 4) <> 2, see A042965, A016825;
all numbers m occur A034178(m) times;
T(n,k) = A004736(n,k)*A094727(n,k).
The row polynomials T(n,x) appear in the calculation of the column g.f.s of triangle A120070 (used to find the frequencies of the spectral lines of the hydrogen atom).
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FORMULA
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Row polynomials: T(n,x) = n^2*sum(x^m,m=0..n)-sum(m^2*x^m,m=0..n) = sum(T(n,k)*x^k,k=0..n-1), n>=1.
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EXAMPLE
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n=3: T(3,x) = 9+8*x+5*x^2
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CROSSREFS
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Sequence in context: A010655 A123596 A094885 this_sequence A131805 A103218 A107381
Adjacent sequences: A094725 A094726 A094727 this_sequence A094729 A094730 A094731
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KEYWORD
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nonn,tabl
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 24 2004
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