A371100 Array A read by upward antidiagonals in which the entry A(n,k) in row n and column k is defined by A(n, k) = 4^n*(6*k - 3 - 2*(-1)^n) + (4^n - 1)/3, n,k >= 1.
21, 21, 45, 341, 117, 69, 341, 725, 213, 93, 5461, 1877, 1109, 309, 117, 5461, 11605, 3413, 1493, 405, 141, 87381, 30037, 17749, 4949, 1877, 501, 165, 87381, 185685, 54613, 23893, 6485, 2261, 597, 189, 1398101, 480597, 283989, 79189, 30037, 8021, 2645, 693, 213, 1398101, 2970965, 873813, 382293, 103765, 36181, 9557, 3029, 789, 237
Offset: 1
Examples
The top left corner of the array: n\k| 1 2 3 4 5 6 7 8 ---+-------------------------------------------------------------------------- 1 | 21, 45, 69, 93, 117, 141, 165, 189, ... 2 | 21, 117, 213, 309, 405, 501, 597, 693, ... 3 | 341, 725, 1109, 1493, 1877, 2261, 2645, 3029, ... 4 | 341, 1877, 3413, 4949, 6485, 8021, 9557, 11093, ... 5 | 5461, 11605, 17749, 23893, 30037, 36181, 42325, 48469, ... 6 | 5461, 30037, 54613, 79189, 103765, 128341, 152917, 177493, ... 7 | 87381, 185685, 283989, 382293, 480597, 578901, 677205, 775509, ... 8 | 87381, 480597, 873813, 1267029, 1660245, 2053461, 2446677, 2839893, ... ...
Links
- Paolo Xausa, Table of n, a(n) for n = 1..11325 (first 150 antidiagonals, flattened).
Crossrefs
Programs
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Mathematica
A371100[n_, k_] := 4^n*(6*k - 3 - 2*(-1)^n) + (4^n - 1)/3; Table[A371100[n - k + 1, k], {n, 10}, {k, n}] (* Paolo Xausa, Apr 21 2024 *)
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PARI
up_to = 55; A371100sq(n,k) = 4^n*(6*k - 3 - 2*(-1)^n) + (4^n - 1)/3; A371100list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A371100sq((a-(col-1)),col))); (v); }; v371100 = A371100list(up_to); A371100(n) = v371100[n];