A376468 Triangle T read by rows: T(n, k) = (n^2 - 2*n + 3 - (-1)^n + n^2 mod 8) / 2 + 4*k.
1, 2, 6, 3, 7, 11, 4, 8, 12, 16, 5, 9, 13, 17, 21, 10, 14, 18, 22, 26, 30, 15, 19, 23, 27, 31, 35, 39, 20, 24, 28, 32, 36, 40, 44, 48, 25, 29, 33, 37, 41, 45, 49, 53, 57, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96
Offset: 0
Examples
Triangle T(n, k) for 0 <= k <= n starts: n \k : 0 1 2 3 4 5 6 7 8 9 10 11 ====================================================== 0 : 1 1 : 2 6 2 : 3 7 11 3 : 4 8 12 16 4 : 5 9 13 17 21 5 : 10 14 18 22 26 30 6 : 15 19 23 27 31 35 39 7 : 20 24 28 32 36 40 44 48 8 : 25 29 33 37 41 45 49 53 57 9 : 34 38 42 46 50 54 58 62 66 70 10 : 43 47 51 55 59 63 67 71 75 79 83 11 : 52 56 60 64 68 72 76 80 84 88 92 96 etc.
Links
- Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of triangle, flattened).
Crossrefs
Cf. A001844
Programs
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Mathematica
Table[Range[#, #+n*4, 4] & [(Mod[n^2, 8] + n*(n-2) - (-1)^n + 3)/2], {n, 0, 15}] (* Paolo Xausa, Nov 13 2024 *) -
PARI
T(n,k)=(n^2-2*n+3-(-1)^n+n^2%8)/2+4*k
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Python
from math import comb, isqrt def A376468(n): return ((a:=(m:=isqrt(k:=n+1<<1))-(k<=m*(m+1)))*(a-2)+3+(1 if a&1 else -1)+(a**2&7)>>1)+(n-comb(a+1,2)<<2) # Chai Wah Wu, Nov 12 2024
Formula
T(n, k) = T(n, k-1) + 4.
T(n+4, 0) = T(n, n) + 4 for n > 3.
T(2*n, n) = 2 * (n^2 + n + 1) - (-1)^n = A001844(n) + 1 - (-1)^n.
Comments