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A047837
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Honaker's triangle problem: form a triangle with base of length n, all entries different, all row sums equal; a(n) gives minimal row sum.
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6
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1, 3, 8, 15, 27, 43, 65, 94, 130, 175, 229, 294, 369, 456, 557, 671, 800, 944, 1105, 1283, 1479, 1695, 1930, 2187, 2465, 2765, 3090, 3439, 3813, 4213, 4641, 5096, 5580, 6095, 6639, 7216, 7825, 8466, 9143, 9855
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OFFSET
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1,2
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COMMENTS
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Suggested by G. L. Honaker, Jr..
Agrees with A047873 at least for n<365, conjectured to always agree.
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REFERENCES
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Pickover, C. A., The Zen of Magic Squares, Circles and Stars: An Exhibition Of Surprising Structures Across Dimensions, Princeton University Press, 2002 (pp. 289-292).
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LINKS
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Table of n, a(n) for n=1..40.
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FORMULA
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Appears to obey a 16-term linear recurrence. - Ralf Stephan, May 06 2004
Empirical G.f.: -x*(x^15 -3*x^14 +3*x^13 -5*x^12 +5*x^11 -9*x^10 +7*x^9 -10*x^8 +7*x^7 -9*x^6 +5*x^5 -6*x^4 +2*x^3 -3*x^2 -1) / ((x-1)^4*(x^2-x+1)*(x^2+1)*(x^2+x+1)^2*(x^4-x^2+1)). - Colin Barker, Jan 18 2013
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EXAMPLE
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Answers for n = 1,2,3,4 are 1 // 3; 1 2 // 8; 2 6; 1 3 4 // 15; 7 8; 4 5 6; 1 2 3 9.
Answer for n = 6 is 43; 21 22; 8 16 19; 5 9 12 17; 3 4 7 14 15; 1 2 6 10 11 13
Answer for n = 7 is 65; 32 33; 20 21 24; 14 15 17 19; 9 10 11 12 23; 5 6 7 13 16 18; 1 2 3 4 8 22 25
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MATHEMATICA
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(* Conjectural *) CoefficientList[(1 + 3*x^2 - 2*x^3 + 6*x^4 - 5*x^5 + 9*x^6 - 7*x^7 + 10*x^8 - 7*x^9 + 9*x^10 - 5*x^11 + 5*x^12 - 3*x^13 + 3*x^14 - x^15)/(1 - 3*x + 4*x^2 - 5*x^3 + 7*x^4 - 8*x^5 + 8*x^6 - 8*x^7 + 8*x^8 - 8*x^9 + 8*x^10 - 8*x^11 + 7*x^12 - 5*x^13 + 4*x^14 - 3*x^15 + x^16) + O[x]^40, x] (* Jean-François Alcover, May 28 2015 *)
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CROSSREFS
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Cf. A047866.
Sequence in context: A034828 A081276 A210979 * A047873 A036419 A054107
Adjacent sequences: A047834 A047835 A047836 * A047838 A047839 A047840
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KEYWORD
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nonn,nice
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AUTHOR
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Jud McCranie
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STATUS
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approved
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