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%I #12 Dec 22 2024 09:08:02
%S 1,13,21,31,233,35,57,403,439,73,121,845,961,805,137,133,1549,1899,
%T 1831,1765,397,183,2753,4011,4017,3943,3025,475,403,2331,4399,7665,
%U 7537,4123,2159,695,307,7919,5945,9709,16177,9365,5737,7635,855,381,5839,12501,10447,17965,18389,10707,13261,5299,901,741,4953,9525,27083,24207,49465,24339,27295,10093,4537,1837
%N Square array A(n, k) = A048720(A065621(sigma((2n-1)^2)), sigma((2k-1)^2)), read by falling antidiagonals, (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), etc.
%H Antti Karttunen, <a href="/A379221/b379221.txt">Table of n, a(n) for n = 1..10440</a>
%H <a href="/index/Con#CongruCrossDomain">Index entries for sequences defined by congruent products between domains N and GF(2)[X]</a>.
%H <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>.
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A(n, k) = A277320(A379223(n), A379223(k)).
%e The top left corner of the array:
%e n\k | 1 2 3 4 5 6 7 8 9
%e (*2-1)^2 | 1 9 25 49 81 121 169 225 289
%e ---------+-------------------------------------------------------------------
%e 1 1 | 1, 13, 31, 57, 121, 133, 183, 403, 307,
%e 2 9 | 21, 233, 403, 845, 1549, 2753, 2331, 7919, 5839,
%e 3 25 | 35, 439, 961, 1899, 4011, 4399, 5945, 12501, 9525,
%e 4 49 | 73, 805, 1831, 4017, 7665, 9709, 10447, 27083, 17515,
%e 5 81 | 137, 1765, 3943, 7537, 16177, 17965, 24207, 50315, 37163,
%e 6 121 | 397, 3025, 4123, 9365, 18389, 49465, 60243, 86471, 108263,
%e 7 169 | 475, 2159, 5737, 10707, 24339, 60215, 52817, 76125, 131005,
%e 8 225 | 695, 7635, 13261, 27295, 51039, 87019, 76565, 245801, 183625,
%e 9 289 | 855, 5299, 10093, 18047, 37823, 107915, 130229, 183305, 200041,
%e 10 361 | 901, 4537, 12003, 22365, 46621, 118545, 98539, 162655, 248191,
%e 11 441 | 1837, 8945, 24187, 43317, 90741, 232729, 201779, 311335, 504583,
%e 12 529 | 1657, 11349, 18231, 40193, 66369, 205597, 231263, 338075, 449339,
%e 13 625 | 1301, 14825, 25235, 56909, 105229, 170945, 156187, 508399, 387535,
%e 14 729 | 3277, 22929, 36059, 81877, 134293, 416121, 464275, 684551, 888103,
%e 15 841 | 1451, 15967, 28601, 50979, 110051, 181895, 139777, 469709, 346669,
%e 16 961 | 1057, 13741, 32767, 58137, 125785, 132133, 182871, 425971, 322387,
%o (PARI)
%o up_to = 66;
%o A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
%o A065621(n) = bitxor(n-1, n+n-1);
%o A379221sq(x,y) = A048720(A065621(sigma((x+x-1)^2)), sigma((y+y-1)^2));
%o A379221list(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] = A379221sq(col,(a-(col-1))))); (v); };
%o v379221 = A379221list(up_to);
%o A379221(n) = v379221[n];
%Y Cf. A000203, A016754, A048720, A065621, A277320.
%Y Cf. A379223 (row 1), A379224 (column 1).
%Y Cf. A379121, A379122, A379123, A379124, A379125.
%Y Cf. also A065768, A379220.
%K nonn,tabl,new
%O 1,2
%A _Antti Karttunen_, Dec 22 2024