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A245300 Triangle read by rows: T(n,k) = (n+k)*(n+k+1)/2 + k, 0 <= k <= n. 5

%I

%S 0,1,4,3,7,12,6,11,17,24,10,16,23,31,40,15,22,30,39,49,60,21,29,38,48,

%T 59,71,84,28,37,47,58,70,83,97,112,36,46,57,69,82,96,111,127,144,45,

%U 56,68,81,95,110,126,143,161,180,55,67,80,94,109,125,142,160

%N Triangle read by rows: T(n,k) = (n+k)*(n+k+1)/2 + k, 0 <= k <= n.

%C T(n,0) = A000217(n);

%C T(n,n) = A046092(n);

%C central terms: T(2*n,n) = A062725(n);

%C sum of row n = A245301(n).

%H Reinhard Zumkeller, <a href="/A245300/b245300.txt">Rows n = 0..125 of triangle, flattened</a>

%e First rows and their row sums (A245301):

%e . 0: 0 0

%e . 1: 1, 4 5

%e . 2: 3, 7, 12 22

%e . 3: 6,11, 17, 24 58

%e . 4: 10,16, 23, 31, 40 120

%e . 5: 15,22, 30, 39, 49, 60 215

%e . 6: 21,29, 38, 48, 59, 71, 84 350

%e . 7: 28,37, 47, 58, 70, 83, 97,112 532

%e . 8: 36,46, 57, 69, 82, 96,111,127,144 768

%e . 9: 45,56, 68, 81, 95,110,126,143,161,180 1065

%e . 10: 55,67, 80, 94,109,125,142,160,179,199,220 1430

%e . 11: 66,79, 93,108,124,141,159,178,198,219,241,264 1870

%e . 12: 78,92,107,123,140,158,177,197,218,240,263,287,312 2392 .

%o (Haskell)

%o a245300 n k = (n + k) * (n + k + 1) `div` 2 + k

%o a245300_row n = map (a245300 n) [0..n]

%o a245300_tabl = map a245300_row [0..]

%o a245300_list = concat a245300_tabl

%Y Cf. A000217, A046092, A062725, A245301.

%K nonn,tabl

%O 0,3

%A _Reinhard Zumkeller_, Jul 17 2014

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Last modified June 1 18:28 EDT 2020. Contains 334762 sequences. (Running on oeis4.)