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A190043
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Number of nondecreasing arrangements of 6 numbers in 0..n with the last equal to n and each after the second equal to the sum of one or two of the preceding three.
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1
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2, 10, 14, 27, 23, 47, 31, 65, 49, 76, 52, 113, 58, 109, 92, 132, 78, 167, 87, 172, 127, 172, 108, 240, 116, 208, 167, 237, 133, 292, 143, 272, 205, 271, 169, 366, 167, 307, 244, 348, 189, 407, 198, 377, 290, 369, 218, 493, 223, 413, 322, 445, 244, 528, 263, 482, 358, 468
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = -4*a(n-1) -11*a(n-2) -23*a(n-3) -40*a(n-4) -59*a(n-5) -75*a(n-6) -81*a(n-7) -71*a(n-8) -42*a(n-9) +4*a(n-10) +59*a(n-11) +112*a(n-12) +150*a(n-13) +164*a(n-14) +150*a(n-15) +112*a(n-16) +59*a(n-17) +4*a(n-18) -42*a(n-19) -71*a(n-20) -81*a(n-21) -75*a(n-22) -59*a(n-23) -40*a(n-24) -23*a(n-25) -11*a(n-26) -4*a(n-27) -a(n-28).
Empirical g.f.: x*(2 + 18*x + 76*x^2 + 239*x^3 + 595*x^4 + 1276*x^5 + 2393*x^6 + 4053*x^7 + 6246*x^8 + 8890*x^9 + 11721*x^10 + 14448*x^11 + 16654*x^12 + 18046*x^13 + 18363*x^14 + 17598*x^15 + 15834*x^16 + 13401*x^17 + 10606*x^18 + 7850*x^19 + 5387*x^20 + 3421*x^21 + 1976*x^22 + 1037*x^23 + 476*x^24 + 189*x^25 + 59*x^26 + 14*x^27) / ((1 - x)^2*(1 + x)^2*(1 - x + x^2)*(1 + x^2)^2*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - Colin Barker, May 04 2018
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EXAMPLE
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All solutions for n=3:
..0....1....1....0....1....0....1....1....1....0....1....2....1....3
..1....2....2....1....1....3....1....3....1....1....1....3....1....3
..1....3....2....1....2....3....1....3....2....1....1....3....1....3
..2....3....3....2....2....3....1....3....3....1....2....3....2....3
..3....3....3....2....3....3....2....3....3....2....3....3....2....3
..3....3....3....3....3....3....3....3....3....3....3....3....3....3
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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