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

Author

Klaus Brockhaus, Apr 02 2010

Keywords

• nonn

Links

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

Crossrefs

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

Programs

Magma

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] ];

Mathematica

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

Formula

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)).