A111568 Triangle read by rows: row n contains n terms of the arithmetic progression having first term 1 and common difference 2[n^(n-1)-1]/(n-1).

1, 1, 3, 1, 9, 17, 1, 43, 85, 127, 1, 313, 625, 937, 1249, 1, 3111, 6221, 9331, 12441, 15551, 1, 39217, 78433, 117649, 156865, 196081, 235297, 1, 599187, 1198373, 1797559, 2396745, 2995931, 3595117, 4194303, 1, 10761681, 21523361, 32285041

Offset

1,3

Comments

Common difference of the row n arithmetic progression = A093461(n) (n>=2). Last term in row n = A093460(n). Sum of terms in row n = n^n=A000312(n).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

T(1, 0)=1; T(n, k)=1+2k[n^(n-1)-1]/(n-1) if n>=2 and 0<=k<n.

Example

Triangle starts:
1;
1,3;
1,9,17;
1,43,85,127;

Maple

T:=proc(n, k) if n=1 and k=0 then 1 elif n>1 and k<n then 1+2*k*(n^(n-1)-1)/(n-1) else 0 fi end: for n from 1 to 9 do seq(T(n, k), k=0..n-1) od; # yields sequence in triangular form

Mathematica

Join[{1}, Flatten[Table[With[{c=2 (n^(n-1)-1)/(n-1)}, NestList[#+c&, 1, n-1]], {n, 2, 10}]]] (* Harvey P. Dale, Mar 19 2026 *)

Crossrefs

Cf. A093460, A093461, A000312.

Sequence in context: A094796 A056843 A076806 * A209324 A121489 A118793

Adjacent sequences: A111565 A111566 A111567 * A111569 A111570 A111571

Keyword

nonn,tabl

Author

Emeric Deutsch, based on Amarnath Murthy's sequence A093460, A093461, Aug 07 2005

Status

approved