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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.

%I A371100 #30 May 12 2024 10:05:46
%S A371100 21,21,45,341,117,69,341,725,213,93,5461,1877,1109,309,117,5461,11605,
%T A371100 3413,1493,405,141,87381,30037,17749,4949,1877,501,165,87381,185685,
%U A371100 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
%N 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.
%H A371100 Paolo Xausa, <a href="/A371100/b371100.txt">Table of n, a(n) for n = 1..11325</a> (first 150 antidiagonals, flattened).
%F A371100 A(n, k) = A007283(n)*A257852(n,k) + A079319(n).
%F A371100 A(n, k) = A371094(A257852(n,k)).
%F A371100 A(n+2, k) = 5 + 16*A(n,k).
%e A371100 The top left corner of the array:
%e A371100 n\k|      1       2       3        4        5        6        7        8
%e A371100 ---+--------------------------------------------------------------------------
%e A371100 1  |     21,     45,     69,      93,     117,     141,     165,     189, ...
%e A371100 2  |     21,    117,    213,     309,     405,     501,     597,     693, ...
%e A371100 3  |    341,    725,   1109,    1493,    1877,    2261,    2645,    3029, ...
%e A371100 4  |    341,   1877,   3413,    4949,    6485,    8021,    9557,   11093, ...
%e A371100 5  |   5461,  11605,  17749,   23893,   30037,   36181,   42325,   48469, ...
%e A371100 6  |   5461,  30037,  54613,   79189,  103765,  128341,  152917,  177493, ...
%e A371100 7  |  87381, 185685, 283989,  382293,  480597,  578901,  677205,  775509, ...
%e A371100 8  |  87381, 480597, 873813, 1267029, 1660245, 2053461, 2446677, 2839893, ...
%e A371100 ...
%t A371100 A371100[n_, k_] := 4^n*(6*k - 3 - 2*(-1)^n) + (4^n - 1)/3;
%t A371100 Table[A371100[n - k + 1, k], {n, 10}, {k, n}] (* _Paolo Xausa_, Apr 21 2024 *)
%o A371100 (PARI)
%o A371100 up_to = 55;
%o A371100 A371100sq(n,k) = 4^n*(6*k - 3 - 2*(-1)^n) + (4^n - 1)/3;
%o A371100 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); };
%o A371100 v371100 = A371100list(up_to);
%o A371100 A371100(n) = v371100[n];
%Y A371100 Cf. A007283, A079319, A257852, A371094, A371101.
%Y A371100 Cf. A372351 (same terms, in different order), A372290 (sorted into ascending order, without duplicates), A372293 (odd numbers that do not occur here).
%Y A371100 Leftmost column is A144864 duplicated, without its initial 1.
%Y A371100 Row 1: A102603.
%K A371100 nonn,tabl
%O A371100 1,1
%A A371100 _Antti Karttunen_ and _Ali Sada_, Apr 18 2024