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A144650 Triangle read by rows where T(m,n) = 2m*n + m + n + 1. 6
5, 8, 13, 11, 18, 25, 14, 23, 32, 41, 17, 28, 39, 50, 61, 20, 33, 46, 59, 72, 85, 23, 38, 53, 68, 83, 98, 113, 26, 43, 60, 77, 94, 111, 128, 145, 29, 48, 67, 86, 105, 124, 143, 162, 181, 32, 53, 74, 95, 116, 137, 158, 179, 200, 221, 35, 58, 81, 104, 127, 150, 173, 196, 219, 242, 265 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
First column: A016789, second column: A016885, third column: A017029, fourth column: A017221, fifth column: A017461. - Vincenzo Librandi, Nov 21 2012
LINKS
Vincenzo Librandi, Rows n = 1..100, flattened
FORMULA
Sum_{n=1..m} T(m, n) = m*(2*m+3)*(m+1)/2 = A160378(n+1) (row sums). - R. J. Mathar, Jan 15 2009, Jan 05 2011
From G. C. Greubel, Oct 14 2023: (Start)
T(n, n) = A001844(n).
T(n, n-1) = A001105(n), n >= 2.
T(n, n-2) = A142463(n-1), n >= 3.
T(n, n-3) = (-1)*A147973(n+2), n >= 4.
Sum_{k=1..n} (-1)^k*T(n, k) = (-1)^n*A007742(floor((n+1)/2)).
G.f.: x*y*(5 - 2*x - 2*x*y - 2*x^2*y + x^2*y^2)/((1-x)^2*(1-x*y)^3). (End)
EXAMPLE
Triangle begins:
5;
8, 13;
11, 18, 25;
14, 23, 32, 41;
17, 28, 39, 50, 61;
20, 33, 46, 59, 72, 85;
23, 38, 53, 68, 83, 98, 113;
26, 43, 60, 77, 94, 111, 128, 145;
29, 48, 67, 86, 105, 124, 143, 162, 181;
32, 53, 74, 95, 116, 137, 158, 179, 200, 221; etc.
MATHEMATICA
T[n_, k_]:= 2 n*k + n + k + 1; Table[T[n, k], {n, 11}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 21 2012 *)
PROG
(Magma) [2*n*k + n + k + 1: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 21 2012
(SageMath) flatten([[2*n*k+n+k+1 for k in range(1, n+1)] for n in range(1, 13)]) # G. C. Greubel, Oct 14 2023
CROSSREFS
Columns k: A016789 (k=1), A016885 (k=2), A017029 (k=3), A017221 (k=4), A017461 (k=5).
Sequence in context: A164128 A259912 A078412 * A046038 A070127 A070128
KEYWORD
nonn,tabl,easy
AUTHOR
Vincenzo Librandi, Jan 13 2009
STATUS
approved

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Last modified May 26 14:36 EDT 2024. Contains 372826 sequences. (Running on oeis4.)