The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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 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. Cf. A000169, A000272, A000312, A036289, A343656, A343658. Sequence in context: A183456 A296313 A183342 * A208342 A157283 A067049 Adjacent sequences: A046685 A046686 A046687 * A046689 A046690 A046691 KEYWORD nonn,tabl,easy AUTHOR N. J. A. Sloane EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Apr 06 2000 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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