A004524 -id:A004524 - cp's OEIS frontend

A130304 Triangle, (1,1,0,0,1,1,0,0,...) in every column.

1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1

Offset: 1

Gary W. Adamson, May 20 2007

			First few rows of the triangle:
  1;
  1, 1;
  0, 1, 1;
  0, 0, 1, 1;
  1, 0, 0, 1, 1;
  1, 1, 0, 0, 1, 1;
  ...

Cf. A004524 (row sums), A130305 (binomial transform).

Missing 0 inserted at a(30) and more terms from Georg Fischer, Jul 28 2023

A347650 Number of minimum total dominating sets in the n-pan graph (for n > 2).

Original entry on oeis.org

1, 2, 3, 2, 3, 8, 5, 2, 5, 18, 7, 2, 7, 32, 9, 2, 9, 50, 11, 2, 11, 72, 13, 2, 13, 98, 15, 2, 15, 128, 17, 2, 17, 162, 19, 2, 19, 200, 21, 2, 21, 242, 23, 2, 23, 288, 25, 2, 25, 338, 27, 2, 27, 392, 29, 2, 29, 450, 31, 2, 31, 512, 33, 2, 33, 578, 35, 2, 35, 648

Offset: 1

Eric W. Weisstein, Sep 09 2021

nonn

Sequence extended to a(1) using the formula/recurrence.

The total domination number is given by A004524(n + 2). - Andrew Howroyd, Jun 11 2025

Eric Weisstein's World of Mathematics, Pan Graph.
Eric Weisstein's World of Mathematics, Minimum Total Dominating Set.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).

Cf. A004524, A302506, A303148.

Table[Piecewise[{{(n + 3)/2, Mod[n, 4] == 3}, {2, Mod[n, 4] == 0}, {(n + 1)/2, Mod[n, 4] == 1}, {(n + 2)^2/8, Mod[n, 4] == 2}}], {n, 20}]
LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {1, 2, 3, 2, 3, 8, 5, 2, 5, 18, 7, 2}, 20]
CoefficientList[Series[(-1 - 2 x - 3 x^2 - 2 x^3 - 2 x^5 + 4 x^6 + 4 x^7 + x^8 - x^10 - 2 x^11)/(-1 + x^4)^3, {x, 0, 20}], x]

a(n) = (n+3)/2   for n = 3 (mod 4)
     = 2         for n = 0 (mod 4)
     = (n+1)/2   for n = 1 (mod 3)
     = (n+2)^2/8 for n = 2 (mod 4).
a(n) = 3*a(n-4)-3*a(n-8)+a(n-12) for n > 12.
G.f.: x*(-1-2*x-3*x^2-2*x^3-2*x^5+4*x^6+4*x^7+x^8-x^10-2*x^11)/(-1+x^4)^3.

A004528 Ratios of successive terms are 1,2,2,2,3,4,4,4,5,6,6,6,7,...

Original entry on oeis.org

1, 1, 2, 4, 8, 24, 96, 384, 1536, 7680, 46080, 276480, 1658880, 11612160, 92897280, 743178240, 5945425920, 53508833280, 535088332800, 5350883328000, 53508833280000, 588597166080000, 7063165992960000

Offset: 0

N. J. A. Sloane

nonn

Cf. A004524.

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A130304 Triangle, (1,1,0,0,1,1,0,0,...) in every column.

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A347650 Number of minimum total dominating sets in the n-pan graph (for n > 2).

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A004528 Ratios of successive terms are 1,2,2,2,3,4,4,4,5,6,6,6,7,...

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