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.

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A052372 Number of nonnegative integer 6 X 6 matrices with sum of elements equal to n, under row and column permutations.

Original entry on oeis.org

1, 1, 4, 10, 33, 91, 298, 881, 2825, 8791, 27947, 87410, 272991, 837370, 2532012, 7496030, 21735743, 61570427, 170399621, 460413115, 1214983434, 3131870712, 7890604652, 19441462894, 46878788710, 110702854983, 256217556777
Offset: 0

Views

Author

Vladeta Jovovic, Mar 08 2000

Keywords

Links

Crossrefs

Row 6 of A318795.
Cf. A002724, A053307.

A052373 Number of nonnegative integer 7 X 7 matrices with sum of elements equal to n, under row and column permutations.

Original entry on oeis.org

1, 1, 4, 10, 33, 91, 298, 910, 2974, 9655, 32287, 108274, 367489, 1246921, 4229171, 14246120, 47542245, 156588539, 507914513, 1618965097, 5064384168, 15531406244, 46670874679, 137372332583, 396053582039, 1118577433593
Offset: 0

Views

Author

Vladeta Jovovic, Mar 08 2000

Keywords

Comments

a(n) = A007716(n) for n=0..7.

Links

Crossrefs

Row 7 of A318795.
Cf. A002724, A053307, A053304.

A202175 Array read by antidiagonals of spreading numbers alpha_n(k).

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 3, 4, 4, 1, 1, 3, 6, 5, 5, 1, 1, 4, 7, 11, 7, 6, 1, 1, 4, 10, 14, 16, 10, 7, 1, 1, 5, 12, 24
Offset: 1

Views

Author

N. J. A. Sloane, Dec 13 2011

Keywords

Examples

			Array begins:
1 1 1 1 1 1 1 1 1 1 ...
1 2 2 3 3 4 4 5 5 6 ...
1 3 4 6 7 10 12 15 19 22 ...
1 4 5 11 14 24 30 45 55 76 ...
1 5 7 16 [26-33] ...
...

Links

Crossrefs

Row 3 is A202169, row 4 is A053307. Cf. A202176.

A258582 a(n) = n*(2*n + 1)*(4*n + 1)/3.

Original entry on oeis.org

0, 5, 30, 91, 204, 385, 650, 1015, 1496, 2109, 2870, 3795, 4900, 6201, 7714, 9455, 11440, 13685, 16206, 19019, 22140, 25585, 29370, 33511, 38024, 42925, 48230, 53955, 60116, 66729, 73810, 81375, 89440, 98021, 107134, 116795, 127020, 137825, 149226, 161239, 173880
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 06 2015

Keywords

Comments

First bisection of the square pyramidal numbers (A000330).

Links

Crossrefs

Cf. A000330, A001477, A005408, A016813, A053126 (partial sums), A100157.

Programs

  • Magma
    [n*(2*n+1)*(4*n+1)/3: n in [0..50]]; // Wesley Ivan Hurt, Nov 17 2015
  • Maple
    A258582:=n->n*(2*n + 1)*(4*n + 1)/3: seq(A258582(n), n=0..50); # Wesley Ivan Hurt, Nov 17 2015
  • Mathematica
    Table[(1/3) n (2 n + 1) (4 n + 1), {n, 0, 45}]
  • PARI
    vector(100, n, n--; n*(2*n+1)*(4*n+1)/3) \\ Altug Alkan, Nov 06 2015
  • PARI
    concat(0, Vec((5*x + 10*x^2 + x^3)/(1 - x)^4 + O(x^50))) \\ Altug Alkan, Nov 06 2015

Formula

G.f.: x*(5 + 10*x + x^2)/(1 - x)^4.
a(n) = A000330(2*n).
Sum_{n>0} 1/a(n) = 3*(6 - Pi - 4*log(2)) = 0.25745587...
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - Vincenzo Librandi, Nov 18 2015
a(n) = A006918(4*n-1) = A053307(4*n-1) = A228706(4*n-1) for n>0. - Bruno Berselli, Nov 18 2015
a(n) = Sum_{k=1..2*n} k^2 (see the first comment). E.g.f. exp(x)*(5*x+ 20*x^2/2+16*x^3/3!). - Wolfdieter Lang, Mar 13 2017
Sum_{n>=1} (-1)^(n+1)/a(n) = 3*log(2) + 6*sqrt(2)*log(1+sqrt(2)) + 3*(sqrt(2)-1/2)*Pi - 18. - Amiram Eldar, Sep 17 2022
Previous Showing 11-14 of 14 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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