A174928 -id:A174928 - cp's OEIS frontend

A174929 Partial sums of A174928.

1, 66, 132, 262, 393, 588, 784, 1044, 1305, 1630, 1956, 2346, 2737, 3192, 3648, 4168, 4689, 5274, 5860, 6510, 7161, 7876, 8592, 9372, 10153, 10998, 11844, 12754, 13665, 14640, 15616, 16656, 17697, 18802, 19908, 21078, 22249, 23484, 24720, 26020

Offset: 0

Klaus Brockhaus, Apr 02 2010

nonn

Index entries for linear recurrences with constant coefficients, signature (2, 0, -2, 1).

Cf. A174928 (partial sums of A174927), A174927 (repeat 1, 64).

T:=&cat[ [1, 64]: n in [0..19] ]; U:=[ n eq 1 select T[1] else Self(n-1)+T[n]: n in [1..#T] ]; [ n eq 1 select U[1] else Self(n-1)+U[n]: n in [1..#U] ];
[ n eq 1 select 1 else n le 3 select 66*(n-1) else Self(n-1)+Self(n-2)-Self(n-3)+65: n in [1..40] ];

LinearRecurrence[{2,0,-2,1},{1,66,132,262},60] (* Harvey P. Dale, Jul 12 2021 *)

a(n) = (71+264*n+130*n^2-63*(-1)^n)/8.
a(n) = a(n-1)+a(n-2)-a(n-3)+65 for n > 2; a(0) = 1, a(1) = 66, a(2) = 132.
G.f.: (1+64*x)/((1-x)^3*(1+x)).

A174927 Periodic sequence: Repeat 1, 64.

Original entry on oeis.org

1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64

Offset: 0

Klaus Brockhaus, Apr 02 2010

Interleaving of A000012 and 2*A010871.
Also continued fraction expansion of (4+sqrt(17))/8.
First differences of A174928.

Index entries for linear recurrences with constant coefficients, signature (0, 1).

Cf. A000012 (all 1's sequence), A010871 (all 32's sequence), A010689 (repeat 1, 8), A174930 (decimal expansion of (4+sqrt(17))/8), A174928.

&cat[ [1, 64]: n in [0..41] ];
[ (65-63*(-1)^n)/2: n in [0..83] ];

PadRight[{},100,{1,64}] (* Harvey P. Dale, Jun 16 2013 *)

a(n) = (65-63*(-1)^n)/2.
a(n) = a(n-2) for n > 1; a(0) = 0, a(1) = 64.
a(n) = -a(n-1)+65 for n > 0; a(0) = 1.
a(n) = ((n+1) mod 2)+64*(n mod 2).
G.f.: (1+64*x)/((1-x)*(1+x)).

cp's OEIS Frontend

A174929 Partial sums of A174928.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula