A135185 Triangle read by rows: E. F. Cornelius Jr. and Phill Schultz-based polynomials for the D_n Cartan Matrices in sequence A129862 that give a triangular sequence.

1, 2, -4, 1, -4, 4, 2, -11, 19, -4, 12, -82, 142, -84, 4, 288, -2208, 4142, -2262, 422, -4, 34560, -277056, 566448, -327528, 49938, -2504, 4, 24883200, -202141440, 427397472, -267303264, 44330580, -1580666, 17368, -4, 125411328000, -1021977907200, 2179398320640, -1397599077312

Offset

1,2

Comments

These polynomials are suggested by Corollary 2.4 in the E. F. Cornelius Jr. and Phill Schultz paper.

It appears that many other fundamental matrix sequences can be related to these Cornelius-Schultz polynomials by a similar treatment.

Here a factor of 4 was necessary to convert them all to integer form.

Links

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

E. F. Cornelius Jr. and Phill Schultz, Sequences Generated by Polynomials, The American Mathematical Monthly, Vol. 115, No. 2 (Feb., 2008), pp. 154-158.

Example

{1},
{2, -4},
{1, -4, 4},
{2, -11, 19, -4},
{12, -82, 142, -84, 4},
{288, -2208, 4142, -2262, 422, -4},
{34560, -277056, 566448, -327528, 49938, -2504, 4},
{24883200, -202141440, 427397472, -267303264, 44330580, -1580666, 17368, -4},

Crossrefs

Cf. A129862.

Sequence in context: A317690 A060047 A379573 * A289460 A377126 A201774

Adjacent sequences: A135182 A135183 A135184 * A135186 A135187 A135188

Keyword

uned,sign,tabl

Author

Roger L. Bagula, Feb 04 2008

Status

approved