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 A332610 Triangle read by rows: T(m,n) = number of triangular regions in a "frame" of size m X n with m >= n >= 1 (see Comments in A331457 for definition of frame). 2
 4, 14, 48, 32, 102, 128, 70, 192, 204, 288, 124, 326, 312, 396, 512, 226, 524, 516, 600, 716, 928, 360, 802, 784, 868, 984, 1196, 1472, 566, 1192, 1196, 1280, 1396, 1608, 1884, 2304, 820, 1634, 1704, 1788, 1904, 2116, 2392, 2812, 3328, 1218, 2296, 2500, 2584, 2700, 2912, 3188, 3608, 4124, 4928 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A331457 for illustrations. LINKS FORMULA The first column is A324042, for which there is an explicit formula. No formula is known for column 2, which is A332606. For m>=n>=3 we have the (new) theorem that T(m,n) = 4*(m^2+n^2)+12*n+4*m-24 + 4*V(m,m,2)+4*V(n,n,2), where V(m,n,q) = Sum_{i = 1..m, j = 1..n, gcd(i,j)=q} (m+1-i)*(n+1-j). EXAMPLE Triangle begins: [4], [14, 48], [32, 102, 128], [70, 192, 204, 288], [124, 326, 312, 396, 512], [226, 524, 516, 600, 716, 928], [360, 802, 784, 868, 984, 1196, 1472], [566, 1192, 1196, 1280, 1396, 1608, 1884, 2304], [820, 1634, 1704, 1788, 1904, 2116, 2392, 2812, 3328], [1218, 2296, 2500, 2584, 2700, 2912, 3188, 3608, 4124, 4928], [1696, 3074, 3456, 3540, 3656, 3868, 4144, 4564, 5080, 5884, 6848], [2310, 4052, 4684, 4768, 4884, 5096, 5372, 5792, 6308, 7112, 8076, 9312], ... CROSSREFS Cf. A331457, A332599, A332600, A324042, A324043, A332606, A332607, A332595, A332596. Sequence in context: A000908 A121095 A264816 * A015651 A022632 A027906 Adjacent sequences:  A332607 A332608 A332609 * A332611 A332612 A332613 KEYWORD nonn,tabl AUTHOR Scott R. Shannon and N. J. A. Sloane, Mar 12 2020 STATUS approved

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Last modified January 19 04:56 EST 2022. Contains 350464 sequences. (Running on oeis4.)