A189375
Expansion of 1/((1-x)^5*(x^3+x^2+x+1)^3).
Original entry on oeis.org
1, 2, 3, 4, 8, 12, 16, 20, 30, 40, 50, 60, 80, 100, 120, 140, 175, 210, 245, 280, 336, 392, 448, 504, 588, 672, 756, 840, 960, 1080, 1200, 1320, 1485, 1650, 1815, 1980, 2200, 2420, 2640, 2860, 3146, 3432, 3718, 4004, 4368
Offset: 0
- Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 3, -6, 3, 0, -3, 6, -3, 0, 1, -2, 1).
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a:= n-> coeff(series(1/((1-x)^5*(x^3+x^2+x+1)^3), x, n+1), x, n):
seq(a(n), n=0..50);
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CoefficientList[Series[1/((1-x)^5(x^3+x^2+x+1)^3),{x,0,50}],x] (* or *) LinearRecurrence[{2,-1,0,3,-6,3,0,-3,6,-3,0,1,-2,1},{1,2,3,4,8,12,16,20,30,40,50,60,80,100},50] (* Harvey P. Dale, Dec 05 2014 *)
A115268
Correlation triangle for floor((n+4)/4).
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 2, 2, 4, 4, 4, 4, 4, 2, 2, 4, 5, 5, 5, 5, 4, 2, 3, 4, 6, 6, 8, 6, 6, 4, 3, 3, 5, 6, 7, 9, 9, 7, 6, 5, 3, 3, 6, 7, 8, 10, 12, 10, 8, 7, 6, 3, 3, 6, 8, 9, 11, 13, 13, 11, 9, 8, 6, 3, 4, 6, 9, 10, 14, 14, 16, 14, 14, 10, 9, 6, 4
Offset: 0
Triangle begins
1;
1,1;
1,2,1;
1,2,2,1;
2,2,3,2,2;
2,3,3,3,3,2;
2,4,4,4,4,4,2;
2,4,5,5,5,5,4,2;
3,4,6,6,8,6,6,4,3;
3,5,6,7,9,9,7,6,5,3;
3,6,7,8,10,12,10,8,7,6,3;
3,6,8,9,11,13,13,11,9,8,6,3;
A366817
Detour index of n body-centered cubic grid unit cells in a row.
Original entry on oeis.org
64, 298, 752, 1476, 2520, 3934, 5768, 8072, 10896, 14290, 18304, 22988, 28392, 34566, 41560, 49424, 58208, 67962, 78736, 90580, 103544, 117678, 133032, 149656, 167600, 186914, 207648, 229852, 253576, 278870, 305784, 334368, 364672, 396746, 430640
Offset: 1
- Paolo Xausa, Table of n, a(n) for n = 1..10000
- Benedek Nagy and H. Mujahed, Detour index for body-centred cubic grid with unit cells connected in a row, Comptes Rendus de l'Académie Bulgare des Sciences, 74(11), 1581-1589 (2021).
- Eric Weisstein's World of Mathematics, Detour Index
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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A366817[n_] := (25*n^3 + 180*n^2 - 13*n)/3; Array[A366817, 50] (* or *)
LinearRecurrence[{4, -6, 4, -1}, {64, 298, 752, 1476}, 50] (* Paolo Xausa, May 28 2024 *)
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a(n) = (25*n^3 + 180*n^2 - 13*n)/3 \\ Andrew Howroyd, Oct 24 2023
Showing 1-3 of 3 results.
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