A158138 Number of nondecreasing integer sequences of length 4 with sum zero and sum of absolute values 2n.
1, 4, 6, 11, 13, 22, 24, 35, 39, 52, 56, 73, 77, 96, 102, 123, 129, 154, 160, 187, 195, 224, 232, 265, 273, 308, 318, 355, 365, 406, 416, 459, 471, 516, 528, 577, 589, 640, 654, 707, 721, 778, 792, 851, 867, 928, 944, 1009, 1025, 1092, 1110, 1179, 1197, 1270, 1288
Offset: 1
Keywords
Examples
For n = 6, we count the possible concatenations of the 4 pairs in the list (-6,0),(-5,-1),(-4,-2),(-3,-3) with their negative reversed correspondants (starting with (-6,0,0,6)), giving (6/2 + 1)^2 = 16 quadruples, plus the 3 quadruples (-6,1,1,4), (-6,1,2,3), (-6,2,2,2) and their 3 negative reversed correspondants, giving a total of 22 possibilities. - _Georg Fischer_, Apr 20 2022
Links
- R. H. Hardin, Table of n, a(n) for n=1..999
Programs
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AWK
# empirical function a(n) { s=1; for(i=1; i
Formula
a(n) = (floor(n/2) + 1)^2 + 2*A069905(n). - Georg Fischer, Apr 20 2022
Comments