A140298 -id:A140298 - cp's OEIS frontend

A140313 First differences of A140298.

1, 0, 0, 1, 1, 1, 1, 4, 4, 1, 13, 13, 1, 40, 40, 1, 121, 121, 1, 364, 364, 1, 1093, 1093, 1, 3280, 3280, 1, 9841, 9841, 1, 29524, 29524, 1, 88573, 88573, 1, 265720, 265720, 1, 797161, 797161, 1, 2391484, 2391484, 1, 7174453, 7174453, 1, 21523360, 21523360, 1, 64570081

Offset: 0

Paul Curtz, May 25 2008

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Cf. A140298

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (x-1)*(x^3+3*x^2+2*x+1)/((3*x^3-1)*(x^2+x+1)) )); // G. C. Greubel, Nov 21 2018

CoefficientList[Series[(x - 1) (x^3 + 3 x^2 + 2 x + 1)/((3 x^3 - 1) (x^2 + x + 1)), {x, 0, 52}], x] (* Michael De Vlieger, Nov 05 2018 *)

Vec((1 - x)*(1 + 2*x + 3*x^2 + x^3)/((1 - 3*x^3)*(1 + x + x^2)) + O(x^40)) \\ Andrew Howroyd, Nov 03 2018

s=((x-1)*(x^3+3*x^2+2*x+1)/((3*x^3-1)*(x^2+x+1))).series(x,50);
s.coefficients(x, sparse=False) # G. C. Greubel, Nov 21 2018

Mix 1, A003462(n), A003462(n).

G.f.: (x - 1)*(x^3 + 3*x^2 + 2*x + 1)/((3*x^3 - 1)*(x^2 + x + 1)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009

Terms a(33) and beyond from Andrew Howroyd, Nov 03 2018

A216220 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=2 or if k-n>=4, T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

Original entry on oeis.org

1, 1, 1, 1, 2, 0, 1, 3, 2, 0, 0, 4, 5, 0, 0, 0, 4, 9, 5, 0, 0, 0, 0, 13, 14, 0, 0, 0, 0, 0, 13, 27, 14, 0, 0, 0, 0, 0, 0, 40, 41, 0, 0, 0, 0, 0, 0, 0, 40, 81, 41, 0, 0, 0, 0, 0, 0, 0, 0, 121, 122, 0, 0, 0, 0, 0

Offset: 0

Philippe Deléham, Mar 13 2013

T(0,2), T(1,1), T(1,2), T(1,3), ... T(n,n), T(n,n+1), T(n,n+2), ... is the sequence A140298.

			Square array begins:
1, 1, 1,  1,  0,  0,   0,   0, 0, ...
1, 2, 3,  4,  4,  0,   0,   0, 0, ...
0, 2, 5,  9, 13, 13,   0,   0, 0, ...
0, 0, 5, 14, 27, 40,  40,   0, 0, ...
0, 0, 0, 14, 41, 81, 121, 121, 0, ...
...

Cf. A000244, A003462, A007051, A038754,

T(n,n) = T(n+1,n) = A007051(n).
T(n,n+1) = 3^n = A000244(n).
T(n,n+2) = T(n,n+3) = A003462(n+1).
Sum_{k, 0<=k<=n} T(n-k,k) = A038754(n).

cp's OEIS Frontend

A140313 First differences of A140298.

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