cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A228272 Volume of sphere (rounded down) with the diameter equal to n.

Original entry on oeis.org

0, 4, 14, 33, 65, 113, 179, 268, 381, 523, 696, 904, 1150, 1436, 1767, 2144, 2572, 3053, 3591, 4188, 4849, 5575, 6370, 7238, 8181, 9202, 10305, 11494, 12770, 14137, 15598, 17157, 18816, 20579, 22449, 24429, 26521, 28730, 31059, 33510, 36086, 38792, 41629, 44602
Offset: 1

Views

Author

K. D. Bajpai, Aug 19 2013

Keywords

Examples

			a(6)=113 since volume is (Pi*n^3)/6 = Pi*6^3/6 = 113.0973355 and floor(113.0973355) = 113.

Links

Crossrefs

Cf. A019673 (Pi/6).
Cf. A066645 (volume with radius n).
Cf. A228189 (similar sequence for right circular cone).

Programs

  • Maple
    a:= n-> floor((Pi*n^3)/6):
seq(a(n),  n=1..100);

Formula

a(n) = floor((Pi*n^3)/6).

A224837 Surface area of Johnson square pyramid (rounded down) with all the edge-lengths equal to n.

Original entry on oeis.org

2, 10, 24, 43, 68, 98, 133, 174, 221, 273, 330, 393, 461, 535, 614, 699, 789, 885, 986, 1092, 1204, 1322, 1445, 1573, 1707, 1846, 1991, 2141, 2297, 2458, 2625, 2797, 2975, 3158, 3346, 3540, 3740, 3945, 4155, 4371, 4592, 4819, 5051, 5289, 5532, 5781, 6035, 6294
Offset: 1

Views

Author

K. D. Bajpai, Sep 18 2013

Keywords

Comments

Johnson square pyramid: a square base with four equilateral triangular-faces. All the edge-lengths are equal.

Examples

			a(3) = 24: Surface area = (1+sqrt(3))*3^2 = 24.588... and floor(24.588...) = 24.

Links

Crossrefs

Cf. A090388, A228189.

Programs

  • Maple
    a:= n-> floor((1+sqrt(3))*n^2):
seq(a(n), n=1..48);
  • Mathematica
    Table[Floor[(1+Sqrt[3])*k^2], {k, 500}]
  • PARI
    vector(500, k, floor((1+sqrt(3))*k^2))
  • PARI
    a(n)=n^2+sqrtint(3*n^4) \\ Charles R Greathouse IV, Sep 18 2013

Formula

a(n) = floor((1+sqrt(3))*n^2).

A228391 Volume of elliptic cone (rounded down) with semi-minor axis = height = n and semi-major axis = 3*n/2.

Original entry on oeis.org

1, 12, 42, 100, 196, 339, 538, 804, 1145, 1570, 2090, 2714, 3451, 4310, 5301, 6433, 7717, 9160, 10774, 12566, 14547, 16725, 19111, 21714, 24543, 27608, 30917, 34482, 38310, 42411, 46795, 51471, 56449, 61738, 67347, 73287, 79565, 86192, 93178, 100530, 108260, 116377
Offset: 1

Views

Author

K. D. Bajpai, Aug 21 2013

Keywords

Examples

			a(9) = 1145 since volume = ((Pi*n*1.5*n)*(n)/3) = ((Pi*9*1.5*9)*(9)/3) = 1145.110522 and floor(1145.110522) = 1145.

Links

Crossrefs

Cf. A228189 (similar sequence for right circular cone).

Programs

  • Maple
    KD := proc() local a; a:= floor(((Pi*n*1.5*n)*(n)/3));
RETURN (a):
end:
seq(KD(),n=1..100);

Formula

a(n) = floor(Pi*n^3/2).

A229063 Volume of the Johnson square pyramid (rounded down) with all the edge lengths equal to n.

Original entry on oeis.org

0, 1, 6, 15, 29, 50, 80, 120, 171, 235, 313, 407, 517, 646, 795, 965, 1158, 1374, 1616, 1885, 2182, 2509, 2867, 3258, 3682, 4142, 4639, 5174, 5748, 6363, 7021, 7723, 8470, 9264, 10105, 10996, 11939, 12933, 13981, 15084, 16244, 17462, 18739, 20078, 21478, 22942
Offset: 1

Views

Author

K. D. Bajpai, Sep 17 2013

Keywords

Comments

Johnson square pyramid: Square base with four equilateral triangular-faces. All the edge lengths are equal to n.

Examples

			a(9)=171:  Volume= sqrt(2)/6*n^3= sqrt(2)/6*9^3= 171.8269478 and floor(171.8269478)= 171.

Links

Crossrefs

Cf. A228189.

Programs

  • Maple
    A229063 := proc(n)
    floor(n^3*sqrt(2)/6) ;
end proc:
  • Mathematica
    Table[Floor[k^3*Sqrt[2]/6],{k,1,100}]

Formula

a(n) = floor(n^3*sqrt(2)/6)
Showing 1-4 of 4 results.

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