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A126890
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Triangle read by rows: T(n,k) = n*(n+2*k+1)/2, 0<=k<=n.
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18
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0, 1, 2, 3, 5, 7, 6, 9, 12, 15, 10, 14, 18, 22, 26, 15, 20, 25, 30, 35, 40, 21, 27, 33, 39, 45, 51, 57, 28, 35, 42, 49, 56, 63, 70, 77, 36, 44, 52, 60, 68, 76, 84, 92, 100, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 55, 65, 75, 85, 95, 105, 115, 125, 135, 145, 155, 66, 77, 88
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OFFSET
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0,3
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COMMENTS
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T(n,k) + T(n,n-k) = A014105(n);
row sums give A059270; Sum(T(n,k): 0<=k<n) = A000578(n);
central terms give A007742; T(2*n+1,n) = A016754(n);
T(n,0) = A000217(n);
T(n,1) = A000096(n) for n>0;
T(n,2) = A055998(n) for n>1;
T(n,3) = A055999(n) for n>2;
T(n,4) = A056000(n) for n>3;
T(n,5) = A056115(n) for n>4;
T(n,6) = A056119(n) for n>5;
T(n,7) = A056121(n) for n>6;
T(n,8) = A056126(n) for n>7;
T(n,10) = A101859(n-1) for n>9;
T(n,n-3) = A095794(n-1) for n>2;
T(n,n-2) = A045943(n-1) for n>1;
T(n,n-1) = A000326(n) for n>0;
T(n,n) = A005449(n).
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REFERENCES
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Léonard Euler, Introduction à l'analyse infinitésimale, tome premier, ACL-Editions, Paris, 1987, p. 353-354
Emile Fourrey, Récréations arithmétiques, Librairie Vuibert, Paris 1899, p. 96
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LINKS
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Table of n, a(n) for n=0..68.
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FORMULA
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T(n,k)=T(n,k-1)+n ,for k<=n [from Philippe Deléham, Oct 03 2011]
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EXAMPLE
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Triangle begins :
0 ;
1, 2 ;
3, 5, 7 ;
6, 9, 12, 15 ;
10, 14, 18, 22, 26 ;
15, 20, 25, 30, 35, 40 ;
21, 27, 33, 39, 45, 51, 57 ;
28, 35, 42, 49, 56, 63, 70, 77 ;... [from Philippe Deléham, Oct 03 2011]
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CROSSREFS
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Cf. A110449.
Sequence in context: A081622 A064143 A115274 * A122637 A076229 A160102
Adjacent sequences: A126887 A126888 A126889 * A126891 A126892 A126893
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KEYWORD
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nonn,tabl
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AUTHOR
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Reinhard Zumkeller, Dec 30 2006
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STATUS
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approved
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