A163657
Triangle T(m,n) = 2*m*n + m + n + 8 read by rows.
Original entry on oeis.org
12, 15, 20, 18, 25, 32, 21, 30, 39, 48, 24, 35, 46, 57, 68, 27, 40, 53, 66, 79, 92, 30, 45, 60, 75, 90, 105, 120, 33, 50, 67, 84, 101, 118, 135, 152, 36, 55, 74, 93, 112, 131, 150, 169, 188, 39, 60, 81, 102, 123, 144, 165, 186, 207, 228, 42, 65, 88, 111, 134, 157, 180
Offset: 1
Triangle begins:
12;
15, 20;
18, 25, 32;
21, 30, 39, 48;
24, 35, 46, 57, 68;
27, 40, 53, 66, 79, 92;
30, 45, 60, 75, 90, 105, 120;
33, 50, 67, 84, 101, 118, 135, 152; etc.
A153049
Numbers n such that 2*n - 13 is not a prime.
Original entry on oeis.org
7, 11, 14, 17, 19, 20, 23, 24, 26, 29, 31, 32, 34, 35, 38, 39, 41, 44, 45, 47, 49, 50, 52, 53, 54, 56, 59, 62, 64, 65, 66, 67, 68, 69, 71, 73, 74, 77, 78, 79, 80, 83, 84, 86, 87, 89, 91, 92, 94, 95, 98, 99, 100, 101, 104, 107, 108, 109, 110, 111, 113, 114, 115, 116
Offset: 1
Distribution of a(n) > 7 in the following triangular array:
11;
14,19;
17,24,31;
20,29,38,47;
23,34,45,56,67;
26,39,52,65,78,91;
29,44,59,74,89,104,119;
32,49,66,83,100,117,134,151;
35,54,73,92,111,130,149,168,187;
38,59,80,101,122,143,164,185,206,227;
41,64,87,110,133,156,179,202,225,248,271;
44,69,94,119,144,169,194,219,244,269,294,319; etc.
which is obtained by (2*h*k + k + h + 7) with h >= k >= 1. - _Vincenzo Librandi_, Jan 15 2013
A163673
a(n) = n*(2*n^2 + 5*n + 15)/2.
Original entry on oeis.org
0, 11, 33, 72, 134, 225, 351, 518, 732, 999, 1325, 1716, 2178, 2717, 3339, 4050, 4856, 5763, 6777, 7904, 9150, 10521, 12023, 13662, 15444, 17375, 19461, 21708, 24122, 26709, 29475, 32426, 35568, 38907, 42449, 46200, 50166
Offset: 0
-
CoefficientList[Series[x*(11-11*x+6*x^2)/(x-1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 11, 33, 72}, 50] (* Vincenzo Librandi, Mar 06 2012 *)
Table[n (2n^2+5n+15)/2,{n,0,60}] (* Harvey P. Dale, Apr 01 2023 *)
-
x='x+O('x^50); concat([0], Vec(x*(11-11*x+6*x^2)/(x-1)^4)) \\ G. C. Greubel, Aug 02 2017
Showing 1-3 of 3 results.
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