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%I #36 Sep 08 2022 08:46:17
%S 0,1,1,2,5,2,3,11,9,3,4,19,20,13,4,5,29,35,29,17,5,6,41,54,51,38,21,6,
%T 7,55,77,79,67,47,25,7,8,71,104,113,104,83,56,29,8,9,89,135,153,149,
%U 129,99,65,33,9,10,109,170,199,202,185,154,115,74,37,10
%N Triangle read by rows: T(n,k) = k*(n-k+1)^2 + n - k, 0 <= k <= n.
%C Mirrored version of a(n) is T(n,k) = (n-k)*(k+1)^2+k, 0 <= k <= n, read by rows:
%C 0
%C 1 1
%C 2 5 2
%C 3 9 11 3
%C 4 13 20 19 4
%C 5 17 29 35 29 5
%C As an infinite square array (matrix) with comments:
%C 0 1 2 3 4 5 A001477
%C 1 5 11 19 29 41 A028387
%C 2 9 20 35 54 77 A014107
%C 3 13 29 51 79 113 A144391
%C 4 17 38 67 104 149 A182868
%C 5 21 47 83 129 185
%e 0; 1,1; 2,5,2; 3,11,9,3; 4,19,20,13,4; 5,29,35,29,17,5; ...
%e As an infinite triangular array:
%e 0
%e 1 1
%e 2 5 2
%e 3 11 9 3
%e 4 19 20 13 4
%e 5 29 35 29 17 5
%e As an infinite square array (matrix) with comments:
%e 0 1 2 3 4 5 A001477
%e 1 5 9 13 17 21 A016813
%e 2 11 20 29 38 47 A017185
%e 3 19 35 51 67 83
%e 4 29 54 79 104 129
%e 5 41 77 113 149 185
%t Table[k (n - k + 1)^(k + #) + n - k &[2 - k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Michael De Vlieger_, Dec 02 2016 *)
%o (Magma) /* As triangle */ [[k*(n-k+1)^2+n-k: k in [0..n]]: n in [0..10]];
%Y Cf. A002064, A001477, A016813, A017185, A062158 (central column). A028387, A014107, A144391, A182868.
%Y Cf. Triangle read by rows: T(n,k) = k*(n-k+1)^m+n-k, 0 <= k <= n: A003056 (m = 0), A059036 (m = 1), A278910 (m = k).
%K nonn,tabl
%O 1,4
%A _Juri-Stepan Gerasimov_, Dec 01 2016