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Triangle read by rows: T(n,m) is the number of cyclic permutations of [n] in which m of successive numbers add to a prime. 0<=m<=n, read by rows n>=0.
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%I #3 Mar 30 2012 17:39:25

%S 0,0,1,0,0,1,0,0,1,0,0,0,2,0,1,0,2,4,4,2,0,1,6,19,16,15,2,1,6,36,84,

%T 108,90,24,12,0,44,230,542,722,602,266,98,14,2,208,1284,3478,5272,

%U 5202,3004,1378,264,70,0,912,6856,21784,39496,46816,35680,20824,6616,2224,184,48

%N Triangle read by rows: T(n,m) is the number of cyclic permutations of [n] in which m of successive numbers add to a prime. 0<=m<=n, read by rows n>=0.

%C The last entry of the (2n)th row is A051252(n). Row sums are apparently in A001710(n-1).

%e The triangle starts

%e n|

%e 0| 0

%e 1| 0 1

%e 2| 0 0 1

%e 3| 0 0 1 0

%e 4| 0 0 2 0 1

%e 5| 0 2 4 4 2 0

%e 6| 1 6 19 16 15 2 1

%e 7| 6 36 84 108 90 24 12 0

%e 8| 44 230 542 722 602 266 98 14 2

%e 9| 208 1284 3478 5272 5202 3004 1378 264 70 0

%e 10| 912 6856 21784 39496 46816 35680 20824 6616 2224 184 48

%e 11| 8016 58232 188160 358080 449424 380592 237888 95280 32880 4776 1072 0

%e 12| 61952 465472 1597312 3298432 4563264 4406592 3152064 1578816 641088 151936 38336 2624 512

%K nonn,tabl

%O 0,13

%A _R. J. Mathar_, Nov 04 2007