

A115310


Triangle read by rows, 0<=k<=n: T(n,k) = if n < 2*k then nk+1 else (k+1)*T(k1+floor((nk+1)/(k+1)),k) + k  (nk+1) mod (k+1).


9



1, 3, 1, 2, 2, 1, 7, 5, 2, 1, 6, 4, 3, 2, 1, 5, 3, 7, 3, 2, 1, 4, 8, 6, 4, 3, 2, 1, 15, 7, 5, 9, 4, 3, 2, 1, 14, 6, 4, 8, 5, 4, 3, 2, 1, 13, 17, 11, 7, 11, 5, 4, 3, 2, 1, 12, 16, 10, 6, 10, 6, 5, 4, 3, 2, 1, 11, 15, 9, 5, 9, 13, 6, 5, 4, 3, 2, 1, 10, 14, 8, 14, 8, 12, 7, 6, 5, 4, 3, 2, 1, 9, 13, 15, 13, 7
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OFFSET

1,2


COMMENTS

The sequences a_k(n) = T(n,k) are selfinverse permutations of the natural numbers:
T(n,1) = A054429(n);
T(n,2) = A115303(n1) for n>1;
T(n,3) = A115304(n2) for n>2;
T(n,4) = A115305(n3) for n>3;
T(n,5) = A115306(n4) for n>4;
T(n,6) = A115307(n5) for n>5;
T(n,7) = A115308(n6) for n>6;
T(n,8) = A115309(n7) for n>7;
T(n,9) = A106649(n8) for n>8;
T(n,k) = nk+1 for k > n/2, especially T(n,n)=1 and T(2*n1,n)=n.


LINKS

Table of n, a(n) for n=1..96.
Index entries for sequences that are permutations of the natural numbers


CROSSREFS

Sequence in context: A016568 A327314 A021888 * A236172 A139381 A225849
Adjacent sequences: A115307 A115308 A115309 * A115311 A115312 A115313


KEYWORD

nonn,tabl


AUTHOR

Reinhard Zumkeller, Jan 20 2006


STATUS

approved



