A332057 Partial sums (and absolute value of first differences) of A332056: if odd (resp. even) add (resp. subtract) the partial sum to get the next term.

1, 3, 2, 3, 7, 4, 5, 11, 6, 7, 15, 8, 9, 19, 10, 11, 23, 12, 13, 27, 14, 15, 31, 16, 17, 35, 18, 19, 39, 20, 21, 43, 22, 23, 47, 24, 25, 51, 26, 27, 55, 28, 29, 59, 30, 31, 63, 32, 33, 67, 34, 35, 71, 36, 37, 75, 38, 39, 79, 40

Offset

1,2

Comments

The terms show a 3-quasiperiodic pattern (2m-1, 4m-1, 2m), m = 1, 2, 3, ...

Or: group positive integers by pairs, then insert the sum of the pair between the two terms.

Links

Antti Karttunen, Table of n, a(n) for n = 1..19683

Eric Angelini, Re: Add or subtract my cumulative sum of terms, SeqFan list, Feb 24 2020.

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

Formula

a(3k-2) = 2k - 1, a(3k-1) = 4k - 1, a(3k) = 2k, for all k >= 1.

From Colin Barker, Feb 25 2020: (Start)

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

a(n) = 2*a(n-3) - a(n-6) for n>6.

(End)

Prog

(PARI) apply( {A332057(n)=n<<max(n%3, 1)\/3}, [1..99])
(PARI) Vec(x*(1 + x)*(1 + 2*x + x^3) / ((1 - x)^2*(1 + x + x^2)^2) + O(x^60)) \\ Colin Barker, Feb 26 2020

Crossrefs

Cf. A332056.

Sequence in context: A136389 A338032 A350770 * A275330 A141863 A071010

Adjacent sequences: A332054 A332055 A332056 * A332058 A332059 A332060

Keyword

nonn,easy

Author

Eric Angelini and M. F. Hasler, Feb 24 2020

Status

approved