A222182
Numbers m such that 2*m + 11 is a square.
Original entry on oeis.org
-5, -1, 7, 19, 35, 55, 79, 107, 139, 175, 215, 259, 307, 359, 415, 475, 539, 607, 679, 755, 835, 919, 1007, 1099, 1195, 1295, 1399, 1507, 1619, 1735, 1855, 1979, 2107, 2239, 2375, 2515, 2659, 2807, 2959, 3115, 3275, 3439, 3607, 3779, 3955, 4135, 4319, 4507, 4699
Offset: 1
After a(2), subsequence of
A168489.
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[m: m in [-5..5000] | IsSquare(2*m+11)];
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I:=[-5,-1,7]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Mar 04 2013
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Table[2 n^2 - 2 n - 5, {n, 50}]
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makelist(coeff(taylor(-(5-14*x+5*x^2)/(1-x)^3, x, 0, n), x, n), n, 0, 50);
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a(n)=2*n^2-2*n-5 \\ Charles R Greathouse IV, Jun 17 2017
A153083
Numbers such that 2*n + 11 is not prime.
Original entry on oeis.org
2, 5, 7, 8, 11, 12, 14, 17, 19, 20, 22, 23, 26, 27, 29, 32, 33, 35, 37, 38, 40, 41, 42, 44, 47, 50, 52, 53, 54, 55, 56, 57, 59, 61, 62, 65, 66, 67, 68, 71, 72, 74, 75, 77, 79, 80, 82, 83, 86, 87, 88, 89, 92, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 107, 110, 112
Offset: 1
Distribution of the terms in the following triangular array:
*
2,7;
5,12,19;
8,17,26,35;
11,22,33,44,55;
14,27,40,53,66,79;
17,32,47,62,77,92,107;
20,37,54,71,88,105,122,139;
23,42,61,80,99,118,137,156,175;
26,47,68,89,110,131,152,173,194,215;
29,52,75,98,121,144,167,190,213,236,259;
32,57,82,107,132,157,182,207,232,257,282,307;
where * marks the decimal values of (2*h*k + k + h - 5) with h >= k >= 1. - _Vincenzo Librandi_, Jan 16 2013
A162258
a(n) = (2*n^3 + 5*n^2 - 9*n)/2.
Original entry on oeis.org
-1, 9, 36, 86, 165, 279, 434, 636, 891, 1205, 1584, 2034, 2561, 3171, 3870, 4664, 5559, 6561, 7676, 8910, 10269, 11759, 13386, 15156, 17075, 19149, 21384, 23786, 26361, 29115, 32054, 35184, 38511, 42041, 45780, 49734, 53909, 58311, 62946, 67820
Offset: 1
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LinearRecurrence[{4, -6, 4, -1}, {-1, 9, 36, 86}, 50] (* or *) CoefficientList[Series[(2+7*x-3*x^2)/(1-x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 04 2012 *)
A324937
Triangle read by rows: T(n, k) = 2*n*k + n + k - 8.
Original entry on oeis.org
-4, -1, 4, 2, 9, 16, 5, 14, 23, 32, 8, 19, 30, 41, 52, 11, 24, 37, 50, 63, 76, 14, 29, 44, 59, 74, 89, 104, 17, 34, 51, 68, 85, 102, 119, 136, 20, 39, 58, 77, 96, 115, 134, 153, 172, 23, 44, 65, 86, 107, 128, 149, 170, 191, 212, 26, 49, 72, 95, 118, 141, 164, 187, 210, 233, 256
Offset: 1
Triangle begins:
-4;
-1, 4;
2, 9, 16;
5, 14, 23, 32;
8, 19, 30, 41, 52;
11, 24, 37, 50, 63, 76;
14, 29, 44, 59, 74, 89, 104;
17, 34, 51, 68, 85, 102, 119, 136;
20, 39, 58, 77, 96, 115, 134, 153, 172; etc.
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[2*n*k+n+k-8: k in [1..n], n in [1..11]]; /* As triangle */ [[2*n*k+n+k-8: k in [1..n]]: n in [1.. 15]];
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t[n_, k_]:=2 n k + n + k - 8; Table[t[n, k], {n, 11}, {k, n}]//Flatten
Showing 1-4 of 4 results.
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