The On-Line Encyclopedia of Integer Sequences (OEIS)

A374822 revision #8

A374822

Antichain-Chain Quilt Numbers: Square table of the number of ASM quilts of type A_2(j) x C_k read down antidiagonals, where C_k is the chain poset or rank k and A_2(j) is the rank 2 poset with a unique minimal and maximal element and j atoms

2, 4, 2, 8, 4, 7, 16, 8, 17, 16, 32, 16, 43, 46, 30, 64, 32, 113, 142, 100, 50, 128, 64, 307, 466, 366, 190, 77, 256, 128, 857, 1606, 1444, 806, 329, 112, 512, 256, 2443, 5746, 6030, 3718, 1589, 532, 156, 1024, 512, 7073, 21142, 26260, 18230, 8393, 2884, 816, 210, 2048, 1024, 20707, 79426, 117966, 93430, 47237, 17164, 4908, 1200, 275, 4096, 2048, 61097, 303046, 542404, 494726, 278249, 109012, 32496, 7932, 1705, 352, 8192, 4096, 181243, 1169746, 2538510, 2684998, 1695029, 725212, 229836, 57828, 12287, 2354, 442, 16384, 8192, 539633, 4554742, 12044020, 14851670, 10592393, 4992484, 1703616, 450660, 97801, 18370, 3172, 546, 32768, 16384, 1610707, 17852386, 57756366, 83384470, 67518437, 35277004, 13072908, 3682020, 832535, 158510, 26650, 4186, 665, 65536, 32768, 4815737, 70322086, 279305764, 473755046, 437200169, 254402932, 103008336, 31153332, 7431985, 1463242, 247780, 37674, 5425, 800, 131072, 65536, 14414443, 278050546, 1359736590, 2717541478, 2867080469, 1864757692, 828707916, 270739668, 68720927, 14167934, 2465242, 375466, 52073, 6920, 952, 262144, 131072, 43177793, 1102537942, 6654800980, 15709845110, 18997064393, 13850340484, 6779099616, 2403012900, 652829881, 142120330, 25730692, 4005066, 553777, 70568, 8704, 1122, 524288, 262144, 129402307, 4381257346, 32708239566, 91395715510, 126948964037, 103996064044, 56214660108, 21693441540, 6335265575, 1464901790, 278268250, 44822986, 6304265, 797624, 93976, 10812, 1311, 1048576, 524288, 387944777, 17438542726, 161307227524, 534498925766, 854359702889, 787943896852, 471424600176, 198578979732, 62545208065, 15427298602, 3092704420, 519829674, 75305905, 9652040, 1124992, 123216, 13281, 1520

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

S. Billey and M. Konvalinka. Generalized Rank Functions and Quilts of Alternating Sign Matrices. Preprint.

LINKS

Table of n, a(n) for n=1..210.

FORMULA

T(j,k)=Sum_{i=2..k} (k+1-i)*i^j for j>=1 and k>1.

T(j,1)=2^j for all j>=1 and k=1.

CROSSREFS

Cf. A374819, A374820, A374821,A374823,A374824.