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

1,2

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