A302588 a(n) = a(n-3) + 7*(n-2), a(0)=1, a(1)=2, a(2)=4.

1, 2, 4, 8, 16, 25, 36, 51, 67, 85, 107, 130, 155, 184, 214, 246, 282, 319, 358, 401, 445, 491, 541, 592, 645, 702, 760, 820, 884, 949, 1016, 1087, 1159, 1233, 1311, 1390, 1471, 1556, 1642, 1730, 1822, 1915, 2010

Offset: 0

Author

Paul Curtz, Jul 17 2018

Keywords

• nonn

Comments

Third of a family after A000124 and A084684. Built from the second differences. The fourth sequence is 1, 2, 4, 8, 16, 32, 49, 91, ..., from periodic [1, 2, 4, 8].

References

• 0

Links

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

Crossrefs

Cf. A069705, A047350 (first differences), A130518.

Programs

Mathematica

CoefficientList[ Series[-(4x^4 +x^3 +x^2 +1)/((x -1)^3 (x^2 +x +1)), {x, 0, 50}], x] (* or *)
LinearRecurrence[{2, -1, 1, -2, 1}, {1, 2, 4, 8, 16}, 50] (* Robert G. Wilson v, Jul 18 2018 *)

Formula

Repeat the second differences of 1, 2, 4, 8, 16, i.e., repeat [1, 2, 4].

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).

a(n) = A069705(n) + 7*A130518(n).