A163674 -id:A163674 - cp's OEIS frontend

A163672 Triangle T(n,m) = 2mn + m + n + 7 read by rows.

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

Offset: 1

Vincenzo Librandi, Aug 03 2009

2*T(n,n) - 13 = (2n+1)^2.

The numbers 2*T(m,n)-13 =(2*n+1)*(2*m+1) are not prime. Also: first column: A016789; second column: A016897; third column: A017017; fourth column: A017185. - Vincenzo Librandi, Nov 20 2012

			Triangle begins:
  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;

Vincenzo Librandi, Rows n = 1..100, flattened

Cf. A016789, A016897, A017017, A017185, A153049, A163674, A163657.

[2*n*k + n + k + 7: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 20 2012

t[n_,k_]:=2 n*k + n + k + 7; Table[t[n, k], {n, 15}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 20 2012 *)

for(n=1,10, for(m=1,n, print1(2*m*n + m + n + 7, ", "))) \\ G. C. Greubel, Aug 02 2017

T(n,m) = A163674(n,m)-2 = A163657(n,m)-1.

Edited by R. J. Mathar, Oct 12 2009

A153051 Numbers n>=9 such that 2*n-17 is not a prime.

Original entry on oeis.org

9, 13, 16, 19, 21, 22, 25, 26, 28, 31, 33, 34, 36, 37, 40, 41, 43, 46, 47, 49, 51, 52, 54, 55, 56, 58, 61, 64, 66, 67, 68, 69, 70, 71, 73, 75, 76, 79, 80, 81, 82, 85, 86, 88, 89, 91, 93, 94, 96, 97, 100, 101, 102, 103, 106, 109, 110, 111, 112, 113, 115, 116, 117, 118, 119

Offset: 1

Vincenzo Librandi, Dec 17 2008

Adding 1 to each entry yields A153041. [From R. J. Mathar, Dec 19 2008]

The terms after a(1) are the values of 2*h*k + k + h + 9, where h and k are positive integers.- Vincenzo Librandi, Jan 19 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A098605, A163674.

[n: n in [9..150] | not IsPrime(2*n - 17)]; // Vincenzo Librandi, Jan 19 2013

Select[Range[9, 200], !PrimeQ[2 # - 17] &] (* Vincenzo Librandi, Jan 19 2013 *)

57 removed by R. J. Mathar, Dec 19 2008

A163675 a(n) = n(2n^2 + 5*n + 19)/2.

Original entry on oeis.org

0, 13, 37, 78, 142, 235, 363, 532, 748, 1017, 1345, 1738, 2202, 2743, 3367, 4080, 4888, 5797, 6813, 7942, 9190, 10563, 12067, 13708, 15492, 17425, 19513, 21762, 24178, 26767, 29535, 32488, 35632, 38973, 42517, 46270, 50238, 54427, 58843, 63492, 68380

Offset: 0

Vincenzo Librandi, Aug 03 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A163674, A162256, A163673.

CoefficientList[Series[x*(13-15*x+8*x^2)/(x-1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 13, 37, 78}, 50] (* Vincenzo Librandi, Mar 06 2012 *)

x='x+O('x^50); concat([0], Vec(x*(13 -15*x +8*x^2)/(x-1)^4)) \\ G. C. Greubel, Aug 02 2017

Row sums from A163674: a(n) = Sum_{m=1..n} (2*m*n + m + n + 9).
a(n) = A163673(n) + 2*n = A162256(n) + 11*n.
G.f.: x*(13 - 15*x + 8*x^2)/(x-1)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
E.g.f.: (1/2)*x*(26 + 11*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 02 2017

Edited and a(31) corrected by R. J. Mathar, Aug 05 2009

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A163672 Triangle T(n,m) = 2mn + m + n + 7 read by rows.

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A153051 Numbers n>=9 such that 2*n-17 is not a prime.

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A163675 a(n) = n(2n^2 + 5*n + 19)/2.

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cp's OEIS Frontend

A163672 Triangle T(n,m) = 2mn + m + n + 7 read by rows.

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Magma

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A153051 Numbers n>=9 such that 2*n-17 is not a prime.

Views

Author

Keywords

Comments

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Crossrefs

Programs

Magma

Mathematica

Extensions

A163675 a(n) = n*(2*n^2 + 5*n + 19)/2.

Views

Author

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Mathematica

PARI

Formula

Extensions

A163675 a(n) = n(2n^2 + 5*n + 19)/2.