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 A221967 T(n,k)=Number of -k..k arrays of length n with the sum ahead of each element differing from the sum following that element by k or less 9
 3, 5, 9, 7, 25, 15, 9, 49, 65, 33, 11, 81, 175, 225, 63, 13, 121, 369, 833, 705, 129, 15, 169, 671, 2241, 3647, 2305, 255, 17, 225, 1105, 4961, 12609, 16513, 7425, 513, 19, 289, 1695, 9633, 34111, 73089, 73983, 24065, 1023, 21, 361, 2465, 17025, 78273, 241153 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ....3.......5.........7..........9..........11...........13............15 ....9......25........49.........81.........121..........169...........225 ...15......65.......175........369.........671.........1105..........1695 ...33.....225.......833.......2241........4961.........9633.........17025 ...63.....705......3647......12609.......34111........78273........159615 ..129....2305.....16513......73089......241153.......653185.......1535745 ..255....7425.....73983.....419841.....1690623......5407233......14661375 ..513...24065....332801....2419713....11888129.....44890625.....140355585 .1023...77825...1495039...13930497....83512319....372332545....1342437375 .2049..251905...6719489...80230401...586864641...3089205249...12843782145 .4095..815105..30195711..462012417..4123582463..25628045313..122870296575 .8193.2637825.135700481.2660655105.28975366145.212618141697.1175482548225 LINKS R. H. Hardin, Table of n, a(n) for n = 1..334 FORMULA Empirical for column k: k=1: a(n) = a(n-1) +2*a(n-2) k=2: a(n) = 3*a(n-1) +2*a(n-2) -4*a(n-3) k=3: a(n) = 3*a(n-1) +8*a(n-2) -4*a(n-3) -8*a(n-4) k=4: a(n) = 5*a(n-1) +8*a(n-2) -20*a(n-3) -8*a(n-4) +16*a(n-5) k=5: a(n) = 5*a(n-1) +18*a(n-2) -20*a(n-3) -48*a(n-4) +16*a(n-5) +32*a(n-6) k=6: a(n) = 7*a(n-1) +18*a(n-2) -56*a(n-3) -48*a(n-4) +112*a(n-5) +32*a(n-6) -64*a(n-7) k=7: a(n) = 7*a(n-1) +32*a(n-2) -56*a(n-3) -160*a(n-4) +112*a(n-5) +256*a(n-6) -64*a(n-7) -128*a(n-8) Empirical for row n: n=1: a(n) = 2*n + 1 n=2: a(n) = 4*n^2 + 4*n + 1 n=3: a(n) = 4*n^3 + 6*n^2 + 4*n + 1 n=4: a(n) = (16/3)*n^4 + (32/3)*n^3 + (32/3)*n^2 + (16/3)*n + 1 n=5: a(n) = (20/3)*n^5 + (50/3)*n^4 + 20*n^3 + (40/3)*n^2 + (16/3)*n + 1 n=6: a(n) = (128/15)*n^6 + (128/5)*n^5 + (112/3)*n^4 + 32*n^3 + (272/15)*n^2 + (32/5)*n + 1 n=7: a(n) = (488/45)*n^7 + (1708/45)*n^6 + (2912/45)*n^5 + (602/9)*n^4 + (2072/45)*n^3 + (952/45)*n^2 + (32/5)*n + 1 EXAMPLE Some solutions for n=6 k=4 ..4...-2....4....1...-4...-1...-2....1...-2...-1....1....3....4....1...-1...-1 .-4....4...-4....0....4....4....3....2....3....2...-2...-4...-2...-3....3....3 ..1...-3....3...-2...-1...-2...-3...-2...-2....2....0....3....1....2....0...-1 ..0....2...-1....3...-2....0....2....2....3...-3....4....1...-3...-2...-2....1 ..3...-4...-2...-3....3....3...-2....1...-1....0...-1...-3....0....3...-3...-2 ..1....1....2....1...-1...-2...-1....1...-1....1....0....1....2...-4....4....2 CROSSREFS Column 1 is A062510(n+1) Column 2 is A189318 Row 2 is A016754 Row 3 is A005917(n+1) Row 4 is A142993 Sequence in context: A166722 A094549 A029642 * A079428 A094548 A112661 Adjacent sequences:  A221964 A221965 A221966 * A221968 A221969 A221970 KEYWORD nonn,tabl AUTHOR R. H. Hardin Feb 01 2013 STATUS approved

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Last modified September 19 00:22 EDT 2021. Contains 347549 sequences. (Running on oeis4.)