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A047837 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. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Suggested by G. L. Honaker, Jr.

Agrees with A047873 at least for n < 365, conjectured to always agree.

REFERENCES

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).

LINKS

Table of n, a(n) for n=1..40.

FORMULA

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

EXAMPLE

a(1)..a(4), 1 // 3; 1 2 // 8; 2 6; 1 3 4 // 15; 7 8; 4 5 6; 1 2 3 9.

a(6) = 43, 21 22; 8 16 19; 5 9 12 17; 3 4 7 14 15; 1 2 6 10 11 13.

a(7) = 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.

CROSSREFS

Cf. A047866.

Sequence in context: A034828 A081276 A210979 * A047873 A036419 A054107

Adjacent sequences:  A047834 A047835 A047836 * A047838 A047839 A047840

KEYWORD

nonn,nice

AUTHOR

Jud McCranie

STATUS

approved

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Last modified May 24 19:38 EDT 2022. Contains 354043 sequences. (Running on oeis4.)