login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Square array A(n,k) = A276945(n,k)/A002110(k-1), read by descending antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
9

%I #15 Oct 27 2019 22:00:30

%S 1,1,3,1,4,4,1,6,6,5,1,8,10,7,7,1,12,14,11,16,9,1,14,22,15,36,19,10,1,

%T 18,26,23,78,41,21,11,1,20,34,27,144,85,45,22,13,1,24,38,35,222,155,

%U 91,46,31,15,1,30,46,39,324,235,165,92,71,34,16,1,32,58,47,438,341,247,166,155,76,36,17,1,38,62,59,668,457,357,248,287,162,80,37,18

%N Square array A(n,k) = A276945(n,k)/A002110(k-1), read by descending antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

%H Antti Karttunen, <a href="/A286625/b286625.txt">Table of n, a(n) for n = 1..1275; the first 50 antidiagonals of array</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F A(n,k) = A276945(n, k) / A002110(k-1).

%e The top left 12 X 12 corner of the array:

%e 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

%e 3, 4, 6, 8, 12, 14, 18, 20, 24, 30, 32, 38

%e 4, 6, 10, 14, 22, 26, 34, 38, 46, 58, 62, 74

%e 5, 7, 11, 15, 23, 27, 35, 39, 47, 59, 63, 75

%e 7, 16, 36, 78, 144, 222, 324, 438, 668, 900, 1148, 1518

%e 9, 19, 41, 85, 155, 235, 341, 457, 691, 929, 1179, 1555

%e 10, 21, 45, 91, 165, 247, 357, 475, 713, 957, 1209, 1591

%e 11, 22, 46, 92, 166, 248, 358, 476, 714, 958, 1210, 1592

%e 13, 31, 71, 155, 287, 443, 647, 875, 1335, 1799, 2295, 3035

%e 15, 34, 76, 162, 298, 456, 664, 894, 1358, 1828, 2326, 3072

%e 16, 36, 80, 168, 308, 468, 680, 912, 1380, 1856, 2356, 3108

%e 17, 37, 81, 169, 309, 469, 681, 913, 1381, 1857, 2357, 3109

%o (Scheme)

%o (define (A286625 n) (A286625bi (A002260 n) (A004736 n)))

%o (define (A286625bi row col) (/ (A276945bi row col) (A002110 (- col 1))))

%Y Transpose: A286623.

%Y Cf. A002110, A276945.

%Y Column 1: A276155.

%Y Row 1: A000012, Row 2: A008864, Row 3: A100484, Row 4: A072055, Row 5: A023523 (from its second term onward), Row 6: A286624.

%Y Cf. A276617 (analogous array).

%K nonn,tabl

%O 1,3

%A _Antti Karttunen_, Jun 28 2017