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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 R. H. Hardin, Table of n, a(n) for n = 1..1196 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 Adjacent sequences: A188274 A188275 A188276 * A188278 A188279 A188280 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.)