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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.
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%I #15 Dec 06 2014 01:34:20

%S 1,3,9,26,73,194,485,1150,2617,5779,12497,26653,56355,118545,248605,

%T 520365,1087853,2272770,4748677,9930475,20800122,43658310,91836751,

%U 193549010,408449129,862455193,1820771343,3840569196,8089327515

%N 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.

%C 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.

%H Reinhard Zumkeller, <a href="/A057153/b057153.txt">Table of n, a(n) for n = 1..150</a>

%F Row sums of triangle A133544. - _Gary W. Adamson_, Sep 14 2007

%e Array begins

%e 1 3 9 26 73 194 ...

%e .2 6 17 47 121 ...

%e . 4 11 30 74 ...

%e .. 7 19 44 ...

%e ... 12 25 ...

%e .... 13 ...

%o (Haskell)

%o a057153 n = a056230_tabl !! (n-1) !! (n-1)

%o -- _Reinhard Zumkeller_, Nov 19 2011

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

%Y Cf. A133544.

%Y Cf. A200379 (first differences).

%K nice,nonn,easy

%O 1,2

%A _Jonas Wallgren_, Jul 30 2000

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