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A329244 Sum of every third term of the Padovan sequence A000931. 1
1, 2, 3, 5, 10, 22, 50, 115, 266, 617, 1433, 3330, 7740, 17992, 41825, 97230, 226031, 525457, 1221538, 2839730, 6601570, 15346787, 35676950, 82938845, 192809421, 448227522, 1042002568, 2422362080, 5631308625, 13091204282, 30433357675, 70748973085, 164471408186 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,3,-1).

FORMULA

a(n) = Sum_{i=0..n} A000931(3*i).

a(n) = A000931(3n+2)+1.

From Colin Barker, Nov 09 2019: (Start)

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

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

(End)

EXAMPLE

For n = 3, a(n) = 1+1+1+2 = 5.

PROG

(Python)

p = lambda x:[1, 0, 0][x] if x<3 else p(x-2)+p(x-3)

a = lambda x:sum(p(3*i) for i in range(x+1))

(PARI) Vec((1 - 2*x) / ((1 - x)*(1 - 3*x + 2*x^2 - x^3)) + O(x^35)) \\ Colin Barker, Nov 09 2019

CROSSREFS

Partial sums of A034943.

Cf. A000931.

Sequence in context: A293842 A014844 A307264 * A173271 A326574 A280019

Adjacent sequences:  A329241 A329242 A329243 * A329245 A329246 A329247

KEYWORD

nonn,easy

AUTHOR

David Nacin, Nov 09 2019

STATUS

approved

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Last modified July 9 22:46 EDT 2020. Contains 335570 sequences. (Running on oeis4.)