A167752 -id:A167752 - cp's OEIS frontend

A167750 Row sums of triangle A167749.

1, 1, 2, 4, 9, 20, 45, 102, 231, 524, 1189, 2699, 6127, 13910, 31581, 71702, 162796, 369622, 839216, 1905419, 4326211, 9822571, 22301948, 50636130, 114968339, 261033373, 592671205, 1345648489, 3055268857, 6936928864, 15750162908

Offset: 0

Paul Barry, Nov 10 2009

Hankel transform is A167752.

			G.f. = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 20*x^5 + 45*x^6 + 102*x^7 + ...

G.f.: 1/(1-x/(1-x/(1-x^2/(1-x^3/(1-x^4/(1-...)))))) (continued fraction);

G.f.: 1/(1-x*f(x)), f(x) the g.f. of A005169.

A237347 First differences of A078633.

Original entry on oeis.org

3, 3, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2

Offset: 1

Reinhard Zumkeller, Mar 18 2014

nonn

a(n) = A078633(n+1) - A078633(n);
2 <= a(n) <= 3;
a(A049068(n)) = 2; a(A002620(n)) = 3;
A237347(n) = abs(A167752(n)) + 2.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

a237347 n = a237347_list !! (n-1)
a237347_list = zipWith (-) (tail a078633_list) a078633_list

A167753 Hankel transform of A167751.

Original entry on oeis.org

1, 1, 0, -1, -1, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1

Offset: 0

Paul Barry, Nov 10 2009

sign

The nonzero terms appear to be indexed by ceiling((n+1)^2/4) - 0^n (see A004652).

Cf. A167752.

cp's OEIS Frontend

A167750 Row sums of triangle A167749.

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A237347 First differences of A078633.

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A167753 Hankel transform of A167751.

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