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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, 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
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.)