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A274602 Triangle read by rows: T(n,k) = k*(n-k+1)^2 + n - k, 0 <= k <= n.

%I A274602 #36 Sep 08 2022 08:46:17
%S A274602 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 A274602 7,55,77,79,67,47,25,7,8,71,104,113,104,83,56,29,8,9,89,135,153,149,
%U A274602 129,99,65,33,9,10,109,170,199,202,185,154,115,74,37,10
%N A274602 Triangle read by rows: T(n,k) = k*(n-k+1)^2 + n - k, 0 <= k <= n.
%C A274602 Mirrored version of a(n) is T(n,k) = (n-k)*(k+1)^2+k, 0 <= k <= n, read by rows:
%C A274602 0
%C A274602 1   1
%C A274602 2   5   2
%C A274602 3   9  11   3
%C A274602 4  13  20  19   4
%C A274602 5  17  29  35  29   5
%C A274602 As an infinite square array (matrix) with comments:
%C A274602 0   1   2   3   4   5                      A001477
%C A274602 1   5  11  19  29  41                      A028387
%C A274602 2   9  20  35  54  77                      A014107
%C A274602 3  13  29  51  79 113                      A144391
%C A274602 4  17  38  67 104 149                      A182868
%C A274602 5  21  47  83 129 185
%e A274602 0; 1,1; 2,5,2; 3,11,9,3; 4,19,20,13,4; 5,29,35,29,17,5; ...
%e A274602 As an infinite triangular array:
%e A274602 0
%e A274602 1   1
%e A274602 2   5   2
%e A274602 3  11   9    3
%e A274602 4  19  20   13    4
%e A274602 5  29  35   29   17    5
%e A274602 As an infinite square array (matrix) with comments:
%e A274602 0   1   2    3    4    5                   A001477
%e A274602 1   5   9   13   17   21                   A016813
%e A274602 2  11  20   29   38   47                   A017185
%e A274602 3  19  35   51   67   83
%e A274602 4  29  54   79  104  129
%e A274602 5  41  77  113  149  185
%t A274602 Table[k (n - k + 1)^(k + #) + n - k &[2 - k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Michael De Vlieger_, Dec 02 2016 *)
%o A274602 (Magma) /* As triangle */ [[k*(n-k+1)^2+n-k: k in [0..n]]: n in [0..10]];
%Y A274602 Cf. A002064, A001477, A016813, A017185, A062158 (central column). A028387, A014107, A144391, A182868.
%Y A274602 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 A274602 nonn,tabl
%O A274602 1,4
%A A274602 _Juri-Stepan Gerasimov_, Dec 01 2016