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 A220556 Square array T(n,k) = ((n+k-1)*(n+k-2)/2+n)^k, n,k > 0 read by antidiagonals. 1
 1, 4, 3, 64, 25, 6, 2401, 512, 81, 10, 161051, 20736, 2197, 196, 15, 16777216, 1419857, 104976, 6859, 400, 21, 2494357888, 148035889, 7962624, 390625, 17576, 729, 28, 500246412961, 21870000000, 887503681, 33554432, 1185921, 39304, 1225, 36 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Column number k of the table T(n,k) is formula for Cantor antidiagonal order in power k LINKS Boris Putievskiy, Table of n, Rows n = 1 to 30 of triangle, flattened Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012. FORMULA As a linear array, the sequence is a(n) = n^A004763 or a(n) = n^((t*t+3*t+4)/2 - n), where t=floor((-1+sqrt(8*n-7))/2). EXAMPLE Square array T(n,k) begins: 1, 4, 64, 2401, 161051, ... 3, 25, 512, 20736, 1419857, ... 6, 81, 2197, 104976, 7962624, ... 10, 196, 6859, 390625, 33554432, ... 15, 400, 17576, 1185921, 115856201, ... 21, 729, 39304, 3111696, 345025251, ... ... The start of the sequence as triangle array is: 1; 4, 3; 64, 25, 6; 2401, 512, 91, 10; 161051, 20736, 2197, 196, 15; ... PROG (Python) t=int((math.sqrt(8*n-7) - 1)/ 2) m=n**((t*t+3*t+4)/2-n) CROSSREFS Column k=1 gives: A000217. Cf. A004736. Sequence in context: A013335 A298314 A299389 * A371687 A299188 A300026 Adjacent sequences: A220553 A220554 A220555 * A220557 A220558 A220559 KEYWORD nonn,tabl AUTHOR Boris Putievskiy, Dec 16 2012 STATUS approved

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Last modified June 24 16:32 EDT 2024. Contains 373679 sequences. (Running on oeis4.)