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
Andrew Howroyd, Table of n, a(n) for n = 0..1325
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
KEYWORD
AUTHOR
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Apr 06 2000
STATUS
approved