A134841
Triangle read by rows: first n terms of n-th row of an array formed by A126988 * A053731(transform).
Original entry on oeis.org
1, 2, 3, 3, 3, 4, 4, 6, 4, 7, 5, 5, 5, 5, 6, 6, 9, 8, 9, 6, 12, 7, 7, 7, 7, 7, 7, 8, 8, 12, 8, 14, 8, 12, 8, 15, 9, 9, 12, 9, 9, 12, 9, 9, 13, 10, 15, 10, 15, 12, 15, 10, 15, 10, 18
Offset: 0
First few terms of the array:
1, 1, 1, 1, 1, 1, 1, ...
2, 3, 2, 3, 2, 3, 2, ...
3, 3, 4, 3, 3, 4, 3, ...
4, 6, 4, 7, 4, 6, 4, ...
5, 5, 5, 5, 5, 6, 5, ...
6, 9, 8, 9, 6, 12, 6, ...
7, 7, 7, 7, 7, 7, 8, ...
...
First few rows of the triangle:
1;
2, 3;
3, 3, 4;
4, 6, 4, 7;
5, 5, 5, 5, 6;
6, 9, 8, 9, 6, 12;
7, 7, 7, 7, 7, 7, 8,
...
A053618
a(n) = ceiling(binomial(n,4)/n).
Original entry on oeis.org
0, 0, 0, 1, 1, 3, 5, 9, 14, 21, 30, 42, 55, 72, 91, 114, 140, 170, 204, 243, 285, 333, 385, 443, 506, 575, 650, 732, 819, 914, 1015, 1124, 1240, 1364, 1496, 1637, 1785, 1943, 2109, 2285, 2470, 2665, 2870, 3086, 3311, 3548, 3795, 4054, 4324
Offset: 1
- Colin Barker, Table of n, a(n) for n = 1..1000
- R. L. Graham and N. J. A. Sloane, Lower bounds for constant weight codes, IEEE Trans. Inform. Theory, 26 (1980), 37-43.
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,1,-3,3,-1).
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[Ceiling(Binomial(n,4)/n): n in [1..60]]; // G. C. Greubel, May 16 2019
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CoefficientList[Series[x^4*(1-x+x^2)*(1-x+x^2+x^4)/((1-x)^3*(1-x^8)), {x,0,60}], x] (* G. C. Greubel, May 16 2019 *)
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concat([0,0,0], Vec(x^4*(x^2-x+1)*(x^4+x^2-x+1) / ((x-1)^4*(x+1)*(x^2+1)*(x^4+1)) + O(x^60))) \\ Colin Barker, Jan 20 2015
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[ceil(binomial(n,4)/n) for n in (1..60)] # G. C. Greubel, May 16 2019
A053733
a(n) = ceiling(binomial(n,9)/n).
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 19, 55, 143, 334, 715, 1430, 2702, 4862, 8398, 13997, 22610, 35530, 54480, 81719, 120175, 173587, 246675, 345345, 476905, 650325, 876525, 1168700, 1542684, 2017356, 2615092, 3362260, 4289780, 5433722
Offset: 1
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- R. L. Graham and N. J. A. Sloane, Lower bounds for constant weight codes, IEEE Trans. Inform. Theory, 26 (1980), 37-43.
- Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-8,28,-56,70,-56,28,-8,1).
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[Ceiling(Binomial(n,9)/n): n in [1..40]]; // G. C. Greubel, Sep 06 2019
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seq(ceil(binomial(n,9)/n), n=1..40); # G. C. Greubel, Sep 06 2019
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Table[Ceiling[Binomial[n, 9]/n], {n, 40}] (* G. C. Greubel, Sep 06 2019 *)
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vector(40, n, ceil(binomial(n,9)/n)) \\ G. C. Greubel, Sep 06 2019
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[ceil(binomial(n,9)/n) for n in (1..40)] # G. C. Greubel, Sep 06 2019
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