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A206492 Sums of rows of the sequence of triangles with nonnegative integers and row widths defined by A004738.

%I A206492 #27 May 21 2021 08:09:03
%S A206492 0,3,3,9,21,19,11,25,45,74,66,49,26,55,90,134,190,170,138,97,50,103,
%T A206492 162,230,310,405,365,310,243,167,85,173,267,370,485,615,763,693,605,
%U A206492 502,387,263,133,269,411,562,725,903,1099,1316,1204,1071,920,754,576,389
%N A206492 Sums of rows of the sequence of triangles with nonnegative integers and row widths defined by A004738.
%C A206492 Row widths: A004738(n): 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5...
%C A206492 Pits: A051925(n+1): 0, 3, 11, 26, 50, 85, 133, 196, 276, 375, 495, 638...
%C A206492 Peak tops: A007290(n+3): 2, 8, 20, 40, 70, 112, 168, 240, 330, 440, 572...
%C A206492 Peak bases: A084990(n+1): 1, 6, 17, 36, 65, 106, 161, 232, 321, 430, 561...
%e A206492 The sequence of triangles begins:
%e A206492 0
%e A206492 1 2
%e A206492 3
%e A206492 4 5
%e A206492 6 7 8
%e A206492 9 10
%e A206492 11
%e A206492 12 13
%e A206492 14 15 16
%e A206492 17 18 19 20
%e A206492 21 22 23
%e A206492 24 25
%e A206492 26
%e A206492 27 28
%e A206492 29 30 31
%e A206492 32 33 34 35
%e A206492 36 37 38 39 40
%e A206492 41 42 43 44
%e A206492 45 46 47
%e A206492 48 49
%e A206492 50
%e A206492 51 52
%o A206492 (Python)
%o A206492 curSign=-1
%o A206492 curLength=sum=0
%o A206492 rowLength=topLength=1
%o A206492 for n in range(1232):
%o A206492     sum += n
%o A206492     curLength += 1
%o A206492     if curLength==rowLength:
%o A206492         print(sum, end=',')
%o A206492         curLength = sum = 0
%o A206492         if rowLength==1 or rowLength==topLength:
%o A206492             curSign = -curSign
%o A206492         topLength += (rowLength==1)
%o A206492         rowLength += curSign
%Y A206492 Cf. A004738, A051925, A007290, A084990.
%Y A206492 Cf. A027480: sums of rows of a triangle with increasing row widths: 0; 1,2; 3,4,5; 6,7,8,9; ...
%K A206492 nonn,easy
%O A206492 1,2
%A A206492 _Alex Ratushnyak_, Jun 28 2012