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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A332056.

Programs

PARI

apply( {A332057(n)=n<
				

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

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)