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A328362 Triangle read by rows: T(n,k) is the sum of all parts k in all partitions of n into consecutive parts, (1 <= k <= n). 6
1, 0, 2, 1, 2, 3, 0, 0, 0, 4, 0, 2, 3, 0, 5, 1, 2, 3, 0, 0, 6, 0, 0, 3, 4, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 8, 0, 2, 3, 8, 5, 0, 0, 0, 9, 1, 2, 3, 4, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 5, 6, 0, 0, 0, 0, 11, 0, 0, 3, 4, 5, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 0, 13, 0, 2, 3, 4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 14 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Iff n is a power of 2 (A000079) then row n lists n - 1 zeros together with n.
Iff n is an odd prime (A065091) then row n lists (n - 3)/2 zeros, (n - 1)/2, (n + 1)/2, (n - 3)/2 zeros, n.
LINKS
FORMULA
T(n,k) = k*A328361(n,k).
EXAMPLE
Triangle begins:
1;
0, 2;
1, 2, 3;
0, 0, 0, 4;
0, 2, 3, 0, 5;
1, 2, 3, 0, 0, 6;
0, 0, 3, 4, 0, 0, 7;
0, 0, 0, 0, 0, 0, 0, 8;
0, 2, 3, 8, 5, 0, 0, 0, 9;
1, 2, 3, 4, 0, 0, 0, 0, 0, 10;
0, 0, 0, 0, 5, 6, 0, 0, 0, 0, 11;
0, 0, 3, 4, 5, 0, 0, 0, 0, 0, 0, 12;
0, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 0, 13;
0, 2, 3, 4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 14;
1, 2, 3, 8,10, 6, 7, 8, 0, 0, 0, 0, 0, 0, 15;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16;
...
For n = 9 there are three partitions of 9 into consecutive parts, they are [9], [5, 4], [4, 3, 2], so the 9th row of triangle is [0, 2, 3, 8, 5, 0, 0, 0, 9].
CROSSREFS
Row sums give A245579.
Column 1 gives A010054, n => 1.
Leading diagonal gives A000027.
Sequence in context: A138262 A276990 A127510 * A158810 A129391 A129390
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Oct 20 2019
STATUS
approved

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Last modified June 16 14:12 EDT 2024. Contains 373430 sequences. (Running on oeis4.)