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A188277 T(n,k) is the number of nondecreasing strings of numbers x(i=1..n) in -k..k with sum x(i)^3 equal to 0, read by antidiagonals. 13
1, 1, 2, 1, 3, 2, 1, 4, 3, 3, 1, 5, 4, 6, 3, 1, 6, 5, 10, 6, 4, 1, 7, 6, 15, 10, 10, 4, 1, 8, 7, 21, 15, 20, 10, 5, 1, 9, 8, 30, 21, 37, 22, 15, 5, 1, 10, 9, 38, 30, 62, 41, 37, 17, 6, 1, 11, 10, 47, 42, 106, 68, 84, 45, 23, 6, 1, 12, 11, 59, 51, 148, 114, 170, 106, 68, 27, 7, 1, 13, 12, 70, 65 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Table starts:
.1..1..1...1...1....1....1....1....1.....1.....1.....1.....1.....1.....1......1
.2..3..4...5...6....7....8....9...10....11....12....13....14....15....16.....17
.2..3..4...5...6....7....8....9...10....11....12....13....14....15....16.....17
.3..6.10..15..21...30...38...47...59....70....82....99...113...128...144....163
.3..6.10..15..21...30...42...51...65....78....92...111...129...152...172....193
.4.10.20..37..62..106..148..197..280...366...470...637...778...922..1098...1327
.4.10.22..41..68..114..202..273..402...548...720...979..1248..1660..2072...2525
.5.15.37..84.170..346..552..817.1319..1951..2817..4262..5776..7388..9688..12753
.5.17.45.106.216..422..890.1415.2401..3809..5725..8810.12622.18662.26200..35595
.6.23.68.186.450.1070.2020.3505.6456.10987.18010.30214.46352.66586.98330.142605
LINKS
FORMULA
T(n,k) = [y^0] [x^n] Product_{j=-k..k} 1/(1-x*y^(j^3)). - Robert Israel, Feb 06 2019
EXAMPLE
Some solutions for n=9, k=8:
-8 -6 -8 -6 -8 -6 -8 -7 -8 -7 -8 -5 -5 -7 -7 -7
-4 -6 -7 -5 -6 -6 -6 -5 -7 -7 -1 -2 -1 -2 -7 -4
-1 -4 -2 -3 -6 -6 -3 -3 -6 -4 -1 -2 -1 -1 -4 -3
0 -3 -1 -1 -4 -3 0 -2 -5 -4 2 0 -1 0 1 1
0 -3 2 -1 -2 0 0 -2 -1 0 2 0 -1 0 1 1
0 -2 4 -1 -2 3 0 -1 -1 4 3 0 0 2 4 3
1 -1 4 1 0 6 3 -1 7 4 4 2 1 4 5 4
4 6 6 3 8 6 6 1 7 7 4 2 4 4 6 5
8 7 8 7 8 6 8 8 8 7 7 5 4 6 7 6
MAPLE
T:= proc(n, k) local P, S, j;
P:= 1/mul(1-x*y^(j^3), j=-k..k);
S:= series(P, x, n+1);
coeff(coeff(S, x, n), y, 0)
end proc:
seq(seq(T(i, m-i), i=1..m-1), m=2..16); # Robert Israel, Feb 06 2019
CROSSREFS
Sequence in context: A278118 A255238 A212536 * A135227 A104325 A204925
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 26 2011
STATUS
approved

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Last modified May 26 05:37 EDT 2024. Contains 372807 sequences. (Running on oeis4.)