A378497 -id:A378497 - cp's OEIS frontend

A378499 a(n) is the number whose base-4 digits are 1 followed by the first n-1 terms of the periodic sequence with initial period 0,3,2.

1, 4, 19, 78, 312, 1251, 5006, 20024, 80099, 320398, 1281592, 5126371, 20505486, 82021944, 328087779, 1312351118, 5249404472, 20997617891, 83990471566, 335961886264, 1343847545059, 5375390180238, 21501560720952, 86006242883811, 344024971535246

Offset: 1

Jonathan Shadrach Gilbert, Nov 28 2024

			a(7) = 1032032_4 = 5006.
a(8) = 10320320_4 = 20024.

Index entries for linear recurrences with constant coefficients, signature (4,0,1,-4).

Cf.: A378497, A037667, A037618, A037681, A378502. Periodic part of sequence rotated left relative to A378497.

Table[FromDigits[Join[{1}, PadRight[{}, n-1, {0, 3, 2}]], 4], {n, 30}]

a(n) = floor((11/36)*4^n).
G.f.: z*(z^3+3*z^2+1)/((z-1)*(4*z-1)*(z^2+z+1)).
E.g.f.: (9 - 20*exp(x) + 11*exp(4*x) + 8*sqrt(3)*exp(-x/2)*sin(sqrt(3)*x/2))/36. - Stefano Spezia, Nov 29 2024

A378502 a(n) is the number whose base-4 digits are 1 followed by the first n-1 terms of the periodic sequence with initial period 3,2,0.

Original entry on oeis.org

1, 7, 30, 120, 483, 1934, 7736, 30947, 123790, 495160, 1980643, 7922574, 31690296, 126761187, 507044750, 2028179000, 8112716003, 32450864014, 129803456056, 519213824227, 2076855296910, 8307421187640, 33229684750563, 132918739002254, 531674956009016

Offset: 1

Jonathan Shadrach Gilbert, Dec 03 2024

			a(7) = 1320320_4 = 7736.
a(8) = 13203203_4 = 30947.

Index entries for linear recurrences with constant coefficients, signature (4,0,1,-4).

Cf. A007090, A378497, A378499, A037667, A037618.

Table[FromDigits[Join[{1}, PadRight[{}, n-1, {3, 2, 0}]], 4], {n, 30}]

a(n) = floor((17/36)*4^n).
G.f.: -x*(x^3-2*x^2-3*x-1)/((x-1)*(4*x-1)*(x^2+x+1)).
a(n) = 4^(n-1) + A037667(n-1) for n > 1.

cp's OEIS Frontend

A378499 a(n) is the number whose base-4 digits are 1 followed by the first n-1 terms of the periodic sequence with initial period 0,3,2.

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