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A277973
Sum of horizontal positions of the first peak in all bargraphs of semiperimeter n.
2
0, 0, 0, 1, 6, 25, 91, 311, 1029, 3346, 10778, 34544, 110444, 352785, 1126885, 3601617, 11521648, 36899528, 118322448, 379908707, 1221423149, 3932113059, 12675055399, 40909511880, 132200481507, 427718677728, 1385419058692, 4492446685542, 14582927712740, 47385785436719
OFFSET
1,5
COMMENTS
Horizontal position is x-coordinate of the start of the leftmost horizontal step of the first peak.
LINKS
A. Blecher, C. Brennan, and A. Knopfmacher, Peaks in bargraphs, Trans. Royal Soc. South Africa, 71, No. 1, 2016, 97-103.
FORMULA
G.f.: (2*x^3*(x^2-sqrt(x^4+2*x^2-4*x+1)+1)) / ((1-x)*(-x^2+sqrt(x^4+2*x^2-4*x+1)-2*x+1)^2).
EXAMPLE
For n = 4, a(4) = 1, as only the bargraph with first column of height one and second column of height two has horizontal position 1, all other cases are zero.
PROG
(PARI) seq(n) = my(r=sqrt((1 - x)*(1 - 3*x - x^2 - x^3) + O(x^(n-2)))); Vec(2*x^3*(1 + x^2 - r) / ((1 - x)*(1 - 2*x - x^2 + r)^2), -n) \\ Andrew Howroyd, Jan 12 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Arnold Knopfmacher, Nov 07 2016
STATUS
approved