A133405 -id:A133405 - cp's OEIS frontend

A133409 Zero followed by partial sums of A133405.

0, 0, 0, 0, 1, 4, 13, 39, 117, 351, 1054, 3163, 9490, 28470, 85410, 256230, 768691, 2306074, 6918223, 20754669, 62264007, 186792021, 560376064, 1681128193, 5043384580, 15130153740, 45390461220, 136171383660

Offset: 0

Paul Curtz, Nov 25 2007

nonn

Index entries for linear recurrences with constant coefficients, signature (4,-3,-1,4,-3).

Cf. A088911, A133405.

Join[{0},Accumulate[LinearRecurrence[{3,0,-1,3},{0,0,0,1},40]]] (* or *) LinearRecurrence[{4,-3,-1,4,-3},{0,0,0,0,1},40] (* Harvey P. Dale, Dec 24 2013 *)

a(n+1)-3*a(n) = A088911(n+3).
a(n) = 4*a(n-1)-3*a(n-2)-a(n-3)+4*a(n-4)-3*a(n-5).
O.g.f.: x^4/((3*x-1)*(1+x)*(x^2-x+1)*(x-1)). - R. J. Mathar, Jul 16 2008

Edited and extended by R. J. Mathar, Jul 16 2008

A139782 Binomial transform of A077947.

Original entry on oeis.org

1, 2, 5, 15, 46, 139, 417, 1250, 3749, 11247, 33742, 101227, 303681, 911042, 2733125, 8199375, 24598126, 73794379, 221383137, 664149410, 1992448229, 5977344687, 17932034062, 53796102187, 161388306561, 484164919682, 1452494759045

Offset: 0

Paul Curtz, May 16 2008

Index entries for linear recurrences with constant coefficients, signature (4,-4,3).

Cf. A010892, A077947, A133405, A122392.

LinearRecurrence[{3,0,-1,3},{1,2,5,15},30] (* Harvey P. Dale, Jan 12 2019 *)

a(n) = 3*a(n-1)-a(n-3)+3*a(n-4).

O.g.f.: -(1-x)^2/((3*x-1)*(x^2-x+1)). a(n) = (4*3^n+3*A010892(n)-A010892(n-1))/7. - R. J. Mathar, May 18 2008

More terms from R. J. Mathar, May 18 2008

cp's OEIS Frontend

A133409 Zero followed by partial sums of A133405.

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