A174927 -id:A174927 - cp's OEIS frontend

A174928 Partial sums of A174927.

1, 65, 66, 130, 131, 195, 196, 260, 261, 325, 326, 390, 391, 455, 456, 520, 521, 585, 586, 650, 651, 715, 716, 780, 781, 845, 846, 910, 911, 975, 976, 1040, 1041, 1105, 1106, 1170, 1171, 1235, 1236, 1300, 1301, 1365, 1366, 1430, 1431, 1495, 1496, 1560

Offset: 0

Klaus Brockhaus, Apr 02 2010

nonn

First differences of A174929.

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

Cf. A174927 (repeat 1, 64), A174929.

T:=&cat[ [1, 64]: n in [0..23] ]; [ n eq 1 select T[1] else Self(n-1)+T[n]: n in [1..#T] ];
[ n le 2 select 64*n-63 else Self(n-2)+65: n in [1..48] ];

a(n) = (67+130*n-63*(-1)^n)/4.
a(n) = a(n-2)+65 for n > 1; a(0) = 1, a(1) = 65.
a(n) = ((n+1) mod 2) + 65*floor((n+1)/2).
G.f.: (1+64*x)/((1-x)^2*(1+x)).

A174930 Decimal expansion of (4+sqrt(17))/8.

Original entry on oeis.org

1, 0, 1, 5, 3, 8, 8, 2, 0, 3, 2, 0, 2, 2, 0, 7, 5, 6, 8, 7, 2, 7, 6, 7, 6, 2, 3, 1, 9, 9, 6, 7, 5, 9, 6, 2, 8, 1, 4, 3, 3, 9, 9, 9, 0, 3, 1, 7, 1, 7, 0, 2, 5, 5, 4, 2, 9, 9, 8, 2, 9, 1, 9, 6, 6, 3, 6, 8, 6, 9, 2, 9, 3, 2, 9, 2, 2, 0, 2, 6, 9, 9, 1, 9, 8, 4, 8, 2, 9, 5, 6, 3, 5, 1, 3, 3, 5, 5, 3, 7, 0, 8, 5, 5, 6

Offset: 1

Klaus Brockhaus, Apr 02 2010

Continued fraction expansion of (4+sqrt(17))/8 is A174927.

			(4+sqrt(17))/8 = 1.01538820320220756872...

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A010473 (decimal expansion of sqrt(17)), A174927 (repeat 1, 64).

A174929 Partial sums of A174928.

Original entry on oeis.org

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)).

cp's OEIS Frontend

A174928 Partial sums of A174927.

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A174930 Decimal expansion of (4+sqrt(17))/8.

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A174929 Partial sums of A174928.

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