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A046688 Antidiagonals of square array in which k-th row (k>0) is an arithmetic progression of difference 2^(k-1). 2
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 5, 5, 1, 1, 5, 7, 9, 9, 1, 1, 6, 9, 13, 17, 17, 1, 1, 7, 11, 17, 25, 33, 33, 1, 1, 8, 13, 21, 33, 49, 65, 65, 1, 1, 9, 15, 25, 41, 65, 97, 129, 129, 1, 1, 10, 17, 29, 49, 81, 129, 193, 257, 257, 1, 1, 11, 19, 33, 57, 97, 161, 257, 385, 513, 513, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
REFERENCES
G. H. Hardy, A Theorem Concerning the Infinite Cardinal Numbers, Quart. J. Math., 35 (1904), p. 90 = Collected Papers, Vol. VII, p. 430.
LINKS
FORMULA
A(m,n) = 1 + n*2^(m-1) for m > 1. - Andrew Howroyd, Mar 07 2020
As a triangle, T(n,k) = A(k,n-k) = 1 + (n-k)*2^(k-1). - Gus Wiseman, May 08 2021
EXAMPLE
From Gus Wiseman, May 08 2021: (Start):
Array A(m,n) = 1 + n*2^(m-1) begins:
n=0: n=1: n=2: n=3: n=4: n=5: n=6: n=7: n=8: n=9:
m=0: 1 1 1 1 1 1 1 1 1 1
m=1: 1 2 3 5 9 17 33 65 129 257
m=2: 1 3 5 9 17 33 65 129 257 513
m=3: 1 4 7 13 25 49 97 193 385 769
m=4: 1 5 9 17 33 65 129 257 513 1025
m=5: 1 6 11 21 41 81 161 321 641 1281
m=6: 1 7 13 25 49 97 193 385 769 1537
m=7: 1 8 15 29 57 113 225 449 897 1793
m=8: 1 9 17 33 65 129 257 513 1025 2049
m=9: 1 10 19 37 73 145 289 577 1153 2305
Triangle T(n,k) = 1 + (n-k)*2^(k-1) begins:
1
1 1
1 2 1
1 3 3 1
1 4 5 5 1
1 5 7 9 9 1
1 6 9 13 17 17 1
1 7 11 17 25 33 33 1
1 8 13 21 33 49 65 65 1
1 9 15 25 41 65 97 129 129 1
1 10 17 29 49 81 129 193 257 257 1
1 11 19 33 57 97 161 257 385 513 513 1
(End)
MATHEMATICA
Table[If[k==0, 1, n*2^(k-1)+1], {n, 0, 9}, {k, 0, 9}] (* ARRAY, Gus Wiseman, May 08 2021 *)
Table[If[k==0, 1, 1+(n-k)*2^(k-1)], {n, 0, 10}, {k, 0, n}] (* TRIANGLE, Gus Wiseman, May 08 2021 *)
PROG
(PARI) A(m, n)={if(m>0, 1+n*2^(m-1), 1)}
{ for(m=0, 10, for(n=0, 10, print1(A(m, n), ", ")); print) } \\ Andrew Howroyd, Mar 07 2020
CROSSREFS
Row sums are A000079.
Diagonal n = m + 1 of the array is A002064.
Diagonal n = m of the array is A005183.
Column m = 1 of the array is A094373.
Diagonal n = m - 1 of the array is A131056.
A002109 gives hyperfactorials (sigma: A260146, omega: A303281).
A009998(k,n) = n^k.
A009999(n,k) = n^k.
A057156 = (2^n)^(2^n).
A062319 counts divisors of n^n.
Sequence in context: A183456 A296313 A183342 * A208342 A157283 A067049
KEYWORD
nonn,tabl,easy
AUTHOR
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Apr 06 2000
STATUS
approved

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Last modified June 18 21:09 EDT 2024. Contains 373487 sequences. (Running on oeis4.)