A061800 -id:A061800 - cp's OEIS frontend

A086954 Binomial transform of A061800.

1, 1, 4, 14, 38, 92, 214, 490, 1108, 2474, 5462, 11948, 25942, 55978, 120148, 256682, 546134, 1157804, 2446678, 5155498, 10835284, 22719146, 47535446, 99265196, 206918998, 430615210, 894784852, 1856678570, 3847574870, 7963585196

Offset: 0

Paul Barry, Jul 25 2003

Index entries for linear recurrences with constant coefficients, signature (5,-9,8,-4).

a(n)=0^n+n2^(n-1)+sum{k=0..floor((n-1)/3) C(n-1, 3k+2) }

O.g.f.: (1-x)(1-3x+5x^2)/[(1-x+x^2)(-1+2x)^2]. - R. J. Mathar, Apr 02 2008

A199408 Triangle T(n,k) = n + k - gcd(n,k) read by rows, 1 <= n, 1 <= k <= n.

Original entry on oeis.org

1, 2, 2, 3, 4, 3, 4, 4, 6, 4, 5, 6, 7, 8, 5, 6, 6, 6, 8, 10, 6, 7, 8, 9, 10, 11, 12, 7, 8, 8, 10, 8, 12, 12, 14, 8, 9, 10, 9, 12, 13, 12, 15, 16, 9, 10, 10, 12, 12, 10, 14, 16, 16, 18, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 11, 12, 12, 12, 12, 16, 12

Offset: 1

Brian Hopkins, Nov 05 2011

A diagonal of an n by k rectangle drawn on a square grid passes through T(n,k) squares: the diagonal enters n squares crossing horizontal segments and enters k squares crossing vertical segments. Gcd(n,k) counts the squares entered at a lattice point, which have been over-counted.

			T(6,4) = 6 + 4 - 2 = 8.
Triangular array begins
  1
  2  2
  3  4  3
  4  4  6  4
  5  6  7  8  5
  6  6  6  8 10  6
  7  8  9 10 11 12  7
  8  8 10  8 12 12 14  8

M. Ollerton, Mathematics Teacher's Handbook, Continuum, 2009, pp. 14-15.

Seiichi Manyama, Rows n = 1..140, flattened
Association of Teachers of Mathematics, Points of Departure 1, Derby, 1972.

Cf. A049627, A074712. Third column A061800.

T(n,k) = n + k - gcd(n,k); \\ Michel Marcus, Aug 04 2018

T(d*a,d*b) = d*T(a,b).

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A086954 Binomial transform of A061800.

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A199408 Triangle T(n,k) = n + k - gcd(n,k) read by rows, 1 <= n, 1 <= k <= n.

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