A057153 Construct difference array so that (1) first row begins with 1, (2) every row is monotonic increasing, (3) no number appears more than once, (4) smallest number not yet used begins a new row. Sequence gives first row of array.

1, 3, 9, 26, 73, 194, 485, 1150, 2617, 5779, 12497, 26653, 56355, 118545, 248605, 520365, 1087853, 2272770, 4748677, 9930475, 20800122, 43658310, 91836751, 193549010, 408449129, 862455193, 1820771343, 3840569196, 8089327515

Offset: 1

Author

Jonas Wallgren, Jul 30 2000

Keywords

• nice
• nonn
• easy

Comments

This is the limit of the family of sequences starting with A005228, A037257, A037260. Adjoin next free number as the first element in a new level of differences unless it would produce a duplicate in which case ignore.

Examples

			Array begins
1 3 9 26 73 194 ...
.2 6 17 47 121 ...
. 4 11 30 74 ...
.. 7 19 44 ...
... 12 25 ...
.... 13 ...
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A057154 (numbers not used), A052474 (main diagonal), A056230 (array). See also A005228, A037257, A037260, A057267, A056231, A056232, A056233, A056234.

Cf. A133544.

Cf. A200379 (first differences).

Programs

Haskell

a057153 n = a056230_tabl !! (n-1) !! (n-1)
-- Reinhard Zumkeller, Nov 19 2011

Formula

Row sums of triangle A133544. - Gary W. Adamson, Sep 14 2007

Extensions

More terms from Rob Speer (rob(AT)twcny.rr.com) and Loren Merritt, Aug 14 2000