A127547
a(n) = 13*n + 4.
Original entry on oeis.org
4, 17, 30, 43, 56, 69, 82, 95, 108, 121, 134, 147, 160, 173, 186, 199, 212, 225, 238, 251, 264, 277, 290, 303, 316, 329, 342, 355, 368, 381, 394, 407, 420, 433, 446, 459, 472, 485, 498, 511, 524, 537, 550, 563, 576, 589, 602, 615, 628, 641, 654, 667, 680, 693, 706, 719
Offset: 0
- P. Sakar, "A Brief History of Cellular Automata," ACM Computing Surveys, vol. 32, pp. 80-107, 2000.
- G. C. Greubel, Table of n, a(n) for n = 0..5000
- C. Langton, Studying Artificial Life with Cellular Automata, Physica D: Nonlinear Phenomena, vol. 22, pp. 120-149, 1986.
- James Propp, Further Ant-ics, Mathematical Intelligencer, 16 pp. 37-42, 1994.
- Index entries for linear recurrences with constant coefficients, signature (2,-1).
A126978
a(n) = 104*n + 9977.
Original entry on oeis.org
9977, 10081, 10185, 10289, 10393, 10497, 10601, 10705, 10809, 10913, 11017, 11121, 11225, 11329, 11433, 11537, 11641, 11745, 11849, 11953, 12057, 12161, 12265, 12369, 12473, 12577, 12681, 12785, 12889, 12993, 13097, 13201, 13305, 13409, 13513, 13617, 13721, 13825
Offset: 0
- B. D. Swan, Table of n, a(n) for n = 0..10000
- C. Langton, Studying Artificial Life with Cellular Automata, Physica D: Nonlinear Phenomena, Vol. 22, 1986, pp. 120-149.
- Ed Pegg Jr, 2D Turing Machines, 2004.
- James Propp, Further Ant-ics, Mathematical Intelligencer, Vol. 16, 1994, pp. 37-42.
- P. Sarkar, A Brief History of Cellular Automata, ACM Computing Surveys. Vol. 32, No. 1, Mar 01 2000, pp. 80-107.
- S. Wolfram, 2D Turing Machines.
- Index entries for linear recurrences with constant coefficients, signature (2,-1).
-
[104*n + 9977: n in [0..40]]; // Vincenzo Librandi, Sep 10 2015
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104*Range[0,40]+9977 (* or *) LinearRecurrence[{2,-1},{9977,10081},40] (* Harvey P. Dale, Dec 16 2011 *)
CoefficientList[Series[(9977 - 9873 x)/(1 - x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 10 2015 *)
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a(n)=104*n+9977 \\ Charles R Greathouse IV, Oct 07 2015
A126979
a(n) = 24*n + 233.
Original entry on oeis.org
233, 257, 281, 305, 329, 353, 377, 401, 425, 449, 473, 497, 521, 545, 569, 593, 617, 641, 665, 689, 713, 737, 761, 785, 809, 833, 857, 881, 905, 929, 953, 977, 1001, 1025, 1049, 1073, 1097, 1121, 1145, 1169, 1193, 1217, 1241, 1265, 1289, 1313, 1337, 1361
Offset: 0
- P. Sakar, "A Brief History of Cellular Automata," ACM Computing Surveys, vol. 32, 2000.
- S. Wolfram, A New Kind of Science, 1st ed. Il.: Wolfram Media Inc., 2002.
-
a:=[233, 257];; for n in [3..60] do a[n]:=2*a[n-1]-a[n-2]; od; a; # G. C. Greubel, May 28 2019
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I:=[233, 257]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..60]]; // G. C. Greubel, May 28 2019
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Table[24*n + 233, {n, 0, 60}] (* Stefan Steinerberger, Jun 17 2007 *)
LinearRecurrence[{2,-1}, {233,257}, 60] (* G. C. Greubel, May 28 2019 *)
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my(x='x+O('x^60)); Vec((233-209*x)/(1-x)^2) \\ G. C. Greubel, May 28 2019
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((233-209*x)/(1-x)^2).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, May 28 2019
A163676
Triangle T(n,m) = 4mn + 2m + 2n - 1 read by rows.
Original entry on oeis.org
7, 13, 23, 19, 33, 47, 25, 43, 61, 79, 31, 53, 75, 97, 119, 37, 63, 89, 115, 141, 167, 43, 73, 103, 133, 163, 193, 223, 49, 83, 117, 151, 185, 219, 253, 287, 55, 93, 131, 169, 207, 245, 283, 321, 359, 61, 103, 145, 187, 229, 271, 313, 355, 397, 439, 67, 113, 159
Offset: 1
Triangle begins:
7;
13, 23;
19, 33, 47;
25, 43, 61, 79;
31, 53, 75, 97, 119;
37, 63, 89, 115, 141, 167;
43, 73, 103, 133, 163, 193, 223;
49, 83, 117, 151, 185, 219, 253, 287;
55, 93, 131, 169, 207, 245, 283, 321, 359;
61, 103, 145, 187, 229, 271, 313, 355, 397, 439;
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[4*n*k + 2*n + 2*k - 1: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 21 2012
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t[n_,k_]:=4 n*k + 2n + 2k - 1; Table[t[n, k], {n, 15}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 21 2012 *)
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for(n=1,10, for(k=1,n, print1(4*n*k + 2*n + 2*k - 1, ", "))) \\ G. C. Greubel, Aug 02 2017
Showing 1-4 of 4 results.
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