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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A007054 A084388 A136389 * 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

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Last modified August 9 18:32 EDT 2020. Contains 336326 sequences. (Running on oeis4.)