A328984 - OEIS

A328984

If n is even, a(n) = floor((5t+1)/2) where t=n/2; if n == 1 (mod 4) then a(n) = 10t+1 where t = (n-1)/4; and if n == 3 (mod 4) then a(n) = 10t+7 where t = (n-3)/4.

1, 3, 7, 5, 11, 8, 17, 10, 21, 13, 27, 15, 31, 18, 37, 20, 41, 23, 47, 25, 51, 28, 57, 30, 61, 33, 67, 35, 71, 38, 77, 40, 81, 43, 87, 45, 91, 48, 97, 50, 101, 53, 107, 55, 111, 58, 117, 60, 121, 63, 127, 65, 131, 68, 137, 70, 141, 73, 147, 75, 151, 78

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OFFSET

1,2

COMMENTS

This is a simplified version of A328190. It does not quite have the defining property of that sequence, which is that the sequence and its first differences together are disjoint. For the present sequence the first differences are in A328985, and the intersection of the sequence and its first differences are the numbers >= 11 that are congruent to 1 (mod 10).

The graphs of A328190 and this sequence are essentially identical.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

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

FORMULA

From Colin Barker, Nov 07 2019: (Start)

G.f.: x*(1 + 3*x + 6*x^2 + 2*x^3 + 3*x^4) / ((1 - x^2)*(1 - x^4)).

a(n) = a(n-2) + a(n-4) - a(n-6) for n > 6.

(End)

MATHEMATICA

Table[Which[EvenQ[n], Floor[(5 n/2+1)/2], Mod[n, 4]==1, 10 (n-1)/4+1, True, 10 (n-3)/4+7], {n, 70}]

CROSSREFS