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.

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

Offset: 1

Author

Jud McCranie

Keywords

• nonn
• nice

Comments

Suggested by G. L. Honaker, Jr.

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

Examples

			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.
		

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).

Crossrefs

Cf. A047866.

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