A277973 Sum of horizontal positions of the first peak in all bargraphs of semiperimeter n.

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

Andrew Howroyd, Table of n, a(n) for n = 1..500

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

Cf. A271941, A273720, A273345, A277999.

Sequence in context: A365531 A099948 A333017 * A143815 A209241 A369360

Adjacent sequences: A277970 A277971 A277972 * A277974 A277975 A277976

Keyword

nonn

Author

Arnold Knopfmacher, Nov 07 2016

Status

approved